
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
Two lines pass through point \(N\) and are tangent to a certain circle with center \(O\). Point \(A\) is taken on one of these lines, and point \(B\) is taken on the other line such that \(OA = OB\) and \(OA > ON\). It is known that \(NA = a\), \(NB = b\), and \(OA = c\) where \(a \neq b\). Find \(ON\).

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