
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 that the focus of the parabola $y^{2}=2px\left(p \gt 0\right)$ is $F$, a line $l$ passing through point $F$ with a slope of $\frac{π}{3}$ intersects the parabola at points $A (located in the first quadrant)$ and $B$. The line $l$ intersects $x=-\frac{p}{2}$ at point $M$. If $\overrightarrow{BM}=t\overrightarrow{MA}$, calculate the value of $t$.

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