
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 point $M$ on the parabola $C$, where $MQ$ is perpendicular to the directrix $l$ at point $Q$. If $\triangle MQF$ is an equilateral triangle, then the value of $\overrightarrow {FQ} \cdot \overrightarrow {FM}$ is \_\_\_\_\_\_.

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