
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 that $P_1, P_2, \ldots, P_{2013}$ are points on the parabola $y^2 = 4x$, with the $x$-coordinates being $x_1, x_2, \ldots, x_{2013}$ respectively. Let $F$ be the focus of the parabola. If $x_1 + x_2 + \ldots + x_{2013} = 10$, then the sum $|P_1F| + |P_2F| + \ldots + |P_{2013}F|$ is equal to.

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