
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Let $ABC$ be a triangle, with $O$ and $I$ being the centers of its circumscribed circle (of radius $R$) and inscribed circle (of radius $r$). Calculate the power of $I$ with respect to the circumscribed circle around $ABC$. Then derive Euler's formula: $\mathrm{OI}^{2}=\mathrm{R}^{2}-2\mathrm{Rr}$.

Present the answer in LaTex format: \boxed{Your answer}
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