
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
Rectangle  $ABCD$  has  $AB = 8$  and  $BC = 13$ . Points  $P_1$  and  $P_2$  lie on  $AB$  and  $CD$  with  $P_1P_2 \parallel BC$ . Points  $Q_1$  and  $Q_2$  lie on  $BC$  and  $DA$  with  $Q_1Q_2 \parallel AB$ . Find the area of quadrilateral  $P_1Q_1P_2Q_2$ .

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