
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 triangle \(ABC\), \(AB = 14\), \(BC = 16\), \(AC = 26\), \(M\) is the midpoint of \(BC\) and \(D\) is the point on \(BC\) such that \(AD\) bisects \(\angle BAC\). Let \(P\) be the foot of the perpendicular from \(B\) onto \(AD\). Determine the length of \(PM\).

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