
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 isosceles triangle \( ABC \) with \( AB = BC \) and base \( AC \), point \( M \) is marked on \( AC \). It is known that \( AM = 7 \), \( MB = 3 \), and \(\angle BMC = 60^\circ \). Find the length of segment \( AC \).

![](https://cdn.mathpix.com/cropped/2024_05_06_22fa77b82e311267ee30g-33.jpg?height=240&width=711&top_left_y=86&top_left_x=369)

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