
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
A tripod has three legs each of length $6$ feet. When the tripod is originally set up, the top of the tripod is $5$ feet from the ground. If 2 feet of one leg break off, let $h$ be the new height of the top of the tripod from the ground when set up with two full legs and one shortened leg. Determine $h$ expressed in the form $\frac m{\sqrt{n}}$, where $m$ and $n$ are positive integers, and $n$ is not divisible by the square of any prime. Find $\lfloor m+\sqrt{n}\rfloor$.

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