
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 a moving point $P(x,y)$ on the ellipse $\dfrac{x^2}{25} + \dfrac{y^2}{16} = 1$, if $F(3,0)$, $|PF|=2$, and $M$ is the midpoint of $PF$, then $|OM|=$ ______.

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