
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 $\frac{x^2}{25} - y^2 = 1$, a point M on the left branch is at a distance of 18 from the right focus F. N is the midpoint of segment MF, and O is the origin of the coordinate system. Find the value of $|ON|$.

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