
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
Trapezoid  $ABCD$  is an isosceles trapezoid with  $AD=BC$ .  Point  $P$  is the intersection of the diagonals  $AC$  and  $BD$ .  If the area of  $\triangle ABP$  is  $50$  and the area of  $\triangle CDP$  is  $72$ , what is the area of the entire trapezoid?

[i]Proposed by David Altizio

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