
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  $ABC$  is right in  $A$  and  $R$  is the midpoint of the hypotenuse  $BC$  . On the major leg  $AB$  the point  $P$  is marked such that  $CP = BP$  and on the segment  $BP$  the point  $Q$  is marked such that the triangle  $PQR$  is equilateral.  If the area of triangle  $ABC$  is  $27$ , calculate the area of triangle  $PQR$  .

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