
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
Let the line $l$ passing through the fixed point $M(a, 0)$ intersect the parabola $y^2 = 4x$ at points $P$ and $Q$. If $\frac{1}{|PM|^2} + \frac{1}{|QM|^2}$ is a constant, then find the value of $a$.

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