
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 $C: y^{2}=4x$ with focus $F$, and a line passing through the point $(-2,0)$ with a slope of $\frac{2}{3}$ intersects the parabola at points $M$ and $N$, calculate the value of the dot product of $\overrightarrow{FM}$ and $\overrightarrow{FN}$.

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