
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 triangle \(ABC\), the lengths of the sides are given: \(AB = 4\), \(BC = 5\), and \(CA = 6\). Point \(M\) is the midpoint of segment \(BC\), and point \(H\) is the foot of the perpendicular dropped from \(B\) to the angle bisector of angle \(A\). Find the length of segment \(HM\). If necessary, round the answer to the nearest hundredth.

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