
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 the hyperbola $x^2 - y^2 = 1$, with $F_1$ and $F_2$ being its two foci, point $P$ is on the right branch of the hyperbola, and $N$ is the midpoint of segment $PF_1$. $O$ is the center of the hyperbola. If $|PF_1| = 5$, then the length of segment $ON$ is ______.

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