
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
Points \(P\), \(Q\), \(R\), \(S\), and \(T\) are located in 3-dimensional space with \(PQ= QR= RS= ST= TP= 3\) and \(\angle PQR = \angle RST = \angle STP = 120^\circ\). The plane of triangle \(PQR\) is parallel to \(\overline{ST}\). What is the area of triangle \(QRS\)?

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