
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
One side of a triangle is $a = 6 \mathrm{~cm}$, the radius of the circumcircle is $r = 5 \mathrm{~cm}$, and the radius of the incircle is $\varrho = 2 \mathrm{~cm}$. Determine the lengths of the sides $b$ and $c$, as well as the area of the triangle, without using a function table.

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