
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, $O$ the center of its circumcircle (with radius $R$), and $I$ the center of its incircle (with radius $r$).

Show Euler's relation: $OI^{2} = R(R - 2r)$. (In particular, $R \geq 2r$.)

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