
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
Let  $ABC$  be a triangle with sides  $AB = 4$  and  $AC = 6$ . Point  $H$  is the projection of vertex  $B$  to the bisector of angle  $A$ . Find  $MH$ , where  $M$  is the midpoint of  $BC$ .

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