
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
Let be given  $ \vartriangle ABC$  with area  $ (\vartriangle ABC) = 60$  cm $^2$ . Let  $R,S $  lie in  $BC$  such that  $BR = RS = SC$  and  $P,Q$  be midpoints of  $AB$  and  $AC$ , respectively. Suppose that  $PS$  intersects  $QR$  at  $T$ . Evaluate area  $(\vartriangle PQT)$ .



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