Right intention, the second link of the path, with right view forms the ‘wisdom’ component. “Compassion” refers to non-ill will and harmlessness. “Emptiness” refers to the end product of renunciation.
“Since the most important formulation of right view is the understanding of the Four Noble Truths, it follows that this view should be in some way determinative of the content of right intention. This we find to be in fact the case. Understanding the four truths in relation to one’s own life gives rise to the intention of renunciation; understanding them in relation to other beings gives rise to the other two right intentions. When we see how our own lives are pervaded by dukkha, and how this dukkha derives from craving, the mind inclines to renunciation — to abandoning craving and the objects to which it binds us. Then, when we apply the truths in an analogous way to other living beings, the contemplation nurtures the growth of good will and harmlessness. We see that, like ourselves, all other living beings want to be happy, and again that like ourselves they are subject to suffering. The consideration that all beings seek happiness causes thoughts of good will to arise — the loving wish that they be well, happy, and peaceful. The consideration that beings are exposed to suffering causes thoughts of harmlessness to arise — the compassionate wish that they be free from suffering.
The moment the cultivation of the Noble Eightfold Path begins, the factors of right view and right intention together start to counteract the three unwholesome roots. Delusion, the primary cognitive defilement, is opposed by right view, the nascent seed of wisdom. The complete eradication of delusion will only take place when right view is developed to the stage of full realization, but every flickering of correct understanding contributes to its eventual destruction. The other two roots (greed, hatred) being emotive defilements, require opposition through the redirecting of intention, and thus meet their antidotes in thoughts of renunciation, good will, and harmlessness.”—-Bikkhu Bodhi, “The Noble Eightfold Path.” (book)
“The Balanced Way” (essay):
My view is that when the Buddha-to-be formulated right intention prior to awakening, there is no mention of action, but an emphasis on thinking:
"And as I remained thus heedful, ardent, & resolute, thinking imbued with non-ill will arose in me. I discerned that 'Thinking imbued with non-ill will has arisen in me; and that leads neither to my own affliction, nor to the affliction of others, nor to the affliction of both. It fosters discernment, promotes lack of vexation, & leads to Unbinding. If I were to think & ponder in line with that even for a night… even for a day… even for a day & night, I do not envision any danger that would come from it, except that thinking & pondering a long time would tire the body. "—MN 19
The awakening was not accomplished through acts of compassion, but rather by meditation and renunciation, withdrawal to the forest. After awakening there was hesitancy to teach, illustrating how his mind was not overly inclined towards compassionate acts. The four noble truths take precedence, and the practice of non-ill will and compassion are dependent on the depth of direct knowledge of them. Most Buddhists already have direct knowledge of the first two noble truths, although often it is not recognized. They know suffering, that’s why the path is sought. That suffering has been brought about by a materialist approach, that’s the second noble truth. But it’s the third noble truth that requires investigation, that renunciation results in release, and that should be personally observed.