
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
If a triangular prism has a base edge of length $l$, width $w$, and a slant height $h$, then the length of its longest edge is equal to $\sqrt{l^2 + w^2 + h^2}$. Suppose $l = 5$ and $h = 13$; if the longest edge is $14$, what is the width $w$?

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