
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
Let $a$ and $b$ be two perpendicular lines, and $MN$ be their common perpendicular segment. Consider a plane $\alpha$ passing through the point $M$ and a point $P$ on line $b$. Let $\theta$ be the angle between $MN$ and the plane $\alpha$, and $\psi$ the angle between $b$ and the plane $\alpha$. If $MN = m$, find the distance from point $P$ to line $a$.

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