
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
We place a 20-filler, a 10-filler, and a 1-crown coin next to each other so that each touches the other two. What is the area of the triangle circumscribed around the coins? \(\left(r_{1}=21 \mathrm{~mm}, r_{2}=19 \mathrm{~mm}, r_{3}=23 \mathrm{~mm}\right)\).

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