
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
In the square \(ABCD\), the bisector of \(\angle CAD\) meets \(CD\) at \(P\) and the bisector of \(\angle ABD\) meets \(AC\) at \(Q\). What is the ratio of the area of triangle \(ACP\) to the area of triangle \(BQA\)?

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