
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_{10}\\) are points on the parabola \\(C\\): \\(y^{2}=4x\\) with their abscissas being \\(x_{1}\\), \\(x_{2}\\), ..., \\(x_{10}\\) respectively, and \\(F\\) is the focus of the parabola \\(C\\), given that \\(x_{1}+x_{2}+…+x_{10}=10\\), then \\(|P_{1}F|+|P_{2}F|+…+|P_{10}F|=\\) ______.

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