
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
Square $ABCD$ has sides of length 6, and $M$ is the midpoint of $\overline{CD}$. A circle with radius 3 and center $M$ intersects a circle with radius 6 and center $A$ at points $P$ and $D$. What is the distance from $P$ to $\overline{AD}$?

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