
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
Consider a square \(ABCD\). Let \(L\) be a point on the diagonal \(AC\). Consider two squares \(APLQ\) and \(CMLN\) contained within the original square, sharing the common vertex \(L\), where point \(P\) lies on the side \(AB\). Let \(O\) be the center of the second square \(CMLN\). Find the angle \(PDO\). Provide the answer in degrees.

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