
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
Rectangle $ABCD$ has dimensions where $AB = 6$ units and $BC = 8$ units. Point $M$ is the midpoint of $\overline{CD}$ and a circle with center $M$ and radius $3$ intersects a circle with center $B$ and radius $5$ at points $P$ and $D$. Determine the distance from $P$ to the line $\overline{AB}$.

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