
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
If $P\_1$, $P\_2$, $P\_3$ are points on the parabola $C$: $y^{2}=8x$, with their abscissas being $x\_1$, $x\_2$, $x\_3$ respectively, and $F$ is the focus of parabola $C$. If $x\_1 + x\_2 + x\_3 = 10$, then find the value of $|P\_1F| + |P\_2F| + |P\_3F| = \_\_\_\_\_\_\_\_$.

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