
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
In the triangle below, \( \angle A\) needs to be the largest angle. For this to happen, the side lengths are given by \( 2x + 5\), \(4x - 3\), and \(x + 15\), where \(2x+5\) corresponds to \(AB\), \(4x-3\) corresponds to \(AC\), and \(x+15\) corresponds to \(BC\). Find the least value of the difference \(n-m\) so that \(m < x < n\), expressed as a common fraction.

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