
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 a triangle, for $\angle P$ to be the largest angle of the triangle, it must satisfy certain side length conditions. The side lengths are given by $x+10$, $x+5$, and $4x$. Determine the least value of $4x - (x+5)$ as a common fraction.

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