
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
Triangle $ABC$ is a right triangle with $\angle ACB$ as its right angle, $m\angle ABC = 45^\circ$, and $AB = 10\sqrt{2}$. Point $P$ is randomly selected inside $ABC$, and extend $\overline{BP}$ to meet $\overline{AC}$ at $D$. Calculate the probability that $BD > 10$.

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