
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
Determine the condition under which the broken-line path from $C$ to $P$ to $D$ is at its shortest and find the length of this path, given that the diameter $\overline{AB}$ of a circle with center $O$ is $18$ units, $C$ is a point $7$ units from $A$, and $D$ is a point $7$ units from $B$, both on $\overline{AB}$.

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