
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 \(\mathcal{P}\) be a parabola with focus \(F\) and directrix \(\ell\). A line through \(F\) intersects \(\mathcal{P}\) at two points \(A\) and \(B\). Let \(D\) and \(C\) be the feet of the altitudes from \(A\) and \(B\) onto \(\ell\), respectively. Given that \(AB = 20\) and \(CD = 14\), compute the area of \(ABCD\).

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