
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 an acute-angled triangle \( ABC \), the altitude \( BH \) and the median \( AM \) are drawn. It is known that the angle \( MCA \) is twice the angle \( MAC \), and \( BC = 10 \).

Find \( AH \).

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