
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 $\triangle ABC$, where $AB = BC > AC$, let $AH$ and $AM$ be the altitude and median to side $BC$, respectively. Given $\frac{S_{\triangle AMH}}{S_{\triangle ABC}} = \frac{3}{8}$, determine the value of $\cos \angle BAC$.

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