
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
The sides  $a,b,c$  of triangle  $ABC$  satisfy  $a\le b\le c$ . The circumradius and inradius of triangle  $ABC$  are  $R$  and  $r$  respectively. Let  $f=a+b-2R-2r$ . Determine the sign of  $f$  by the measure of angle  $C$ .

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