
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
Points \( A \) and \( B \) lie on circle \(\omega\). Point \( P \) lies on the extension of segment \( AB \) past \( B \). Line \(\ell \) passes through \( P \) and is tangent to \(\omega\). The tangents to \(\omega\) at points \( A \) and \( B \) intersect \(\ell\) at points \( D \) and \( C \) respectively. Given that \( AB = 7 \), \( BC = 2 \), and \( AD = 3 \), compute \( BP \).

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