
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 width 6 and height 3. Point $M$ is the midpoint of $\overline{CD}$. A circle with radius 1.5 and center $M$ intersects a circle with radius 5 and center $A$. Determine the coordinates of point $P$, where $P$ is one of the intersection points. Additionally, calculate the distance from point $P$ to $\overline{AD}$.

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