
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
Segments \( AM \) and \( BH \) are the median and altitude, respectively, of an acute-angled triangle \( ABC \). It is known that \( AH = 1 \) and \( 2 \angle MAC = \angle MCA \). Find the side \( BC \).

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