
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 $P_{1}$, $P_{2}$, ..., $P_{8}$ are points on the parabola $y^{2}=4x$ with their abscissas being $x_{1}$, $x_{2}$, ..., $x_{8}$ respectively, and $F$ is the focus of the parabola, given that $x_{1}$, $x_{2}$, ..., $x_{n} (n \in \mathbb{N}^*)$ form an arithmetic sequence and $x_{1}+x_{2}+…+x_{9}=45$, calculate the distance $|P_{5}F|$.

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