
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 a point $P(a,0)$ on the $x$-axis, a line passing through $P$ intersects the parabola $y^{2}=8x$ at points $A$ and $B$. If $\frac{1}{|AP^{2}|}+ \frac{1}{|BP^{2}|}$ is a constant value, find the value of the real number $a$.

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