思いやり and 同情: thoughtfulness and sympathy for someone's circumstances
Compare thoughtfulness sensed in a remark with sympathy felt on hearing someone's circumstances, preserving a proposal to consider support rather than completed assistance.
Consideration for another person's position
思いやり (おもいやり) means consideration or compassion. “相手の立場を考える思いやりが大切だ。” says that consideration for the other person's position is important.
In “彼女の何気ない一言に深い思いやりを感じた。”, the speaker sensed deep thoughtfulness in her casual remark. 何気ない modifies her remark; it does not establish whether that remark was malicious or accidental.
Sympathy on hearing someone's circumstances
同情 (どうじょう) means sympathy or compassion. “事情を聞くうちに彼女へ深い同情を覚えた。” describes feeling deep sympathy for her while hearing about her circumstances.
“同情するだけでなく必要な支援を考えよう。” proposes considering the support needed rather than merely offering sympathy. It states a proposal to think about support, not assistance already provided.
Overlapping feelings and the extent of action
Consideration for another person's position and sympathy for their circumstances can coexist. Do not define 思いやり as containing no sympathy or 同情 as containing no consideration.
Distinguish feeling sympathy, sensing thoughtfulness in a remark, and proposing consideration of support. Neither the reaction nor the proposal establishes that practical help was already provided.
Does 必要な支援を考えよう mean that the needed assistance has already been provided?
Show the answer and why
No. It proposes thinking about the support needed instead of stopping at sympathy. Feeling sympathy on hearing the circumstances is distinct from actually providing support.

