
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
ABC is a triangle with side lengths |BC| = a, |CA| = b, |AB| = c, circumradius R, and inradius r. Given that a ≤ b ≤ c, determine the values of angle C for which a + b - 2(r + R) is positive, negative, or zero.

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