
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 triangle  $ ABC$  has semiperimeter  $ p$ . Find the side length  $ BC$  and the area  $ S$  in terms of  $ \angle A$ ,  $ \angle B$  and  $ p$ . In particular, find  $ S$  if  $ p \approx 23.6$ ,  $ \angle A \approx 52^{\circ}42'$ ,  $ \angle B \approx 46^{\circ}16'$ .

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