
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 the three walls forming the corner of a classroom are denoted as $\alpha$, $\beta$, $\gamma$, and their intersecting lines as $BA$, $BC$, $BD$, and a point $P$ inside the classroom is at distances of $3m$, $4m$, and $1m$ from the three walls $\alpha$, $\beta$, $\gamma$ respectively, then the distance from $P$ to the corner $B$ is _______ $m$.

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