
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
In \( \triangle ABC \), \( \angle B = 60^\circ \), \( \angle C = 90^\circ \), and \( AB = 1 \). \( B C P \), \( CA Q \), and \( AB R \) are equilateral triangles outside \( \triangle ABC \). \( QR \) meets \( AB \) at \( T \). Find the area of \( \triangle PRT \).

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