
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 \(ABCD\) be a convex quadrilateral whose diagonals \(AC\) and \(BD\) meet at \(P\). Let the area of triangle \(APB\) be 24 and let the area of triangle \(CPD\) be 25. What is the minimum possible area of quadrilateral \(ABCD\)?

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