
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
Given the parabola $C: y^2 = 2px$ ($p > 0$) with directrix $l$, a line passing through $M(1, 0)$ with a slope of $\sqrt{3}$ intersects $l$ at point $A$ and intersects $C$ at one point $B$. If $\overrightarrow{AM} = \overrightarrow{MB}$, calculate the value of $p$.

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