
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 \(ABC\) has \(\angle A = 90^\circ\), side \(BC = 25\), \(AB > AC\), and area 150. Circle \(\omega\) is inscribed in \(ABC\), with \(M\) as its point of tangency on \(AC\). Line \(BM\) meets \(\omega\) a second time at point \(L\). Find the length of segment \(BL\).

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