
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
In an equilateral triangle \( \triangle ABC \) with a side length of \( \sqrt{3} \), point \( D \) is on the circumcircle of \( \triangle ABC \) and satisfies \( AD = \sqrt{2} \). Let \( P \) be a moving point on \( \triangle ABC \). Determine the range of \( \overrightarrow{PA} \cdot \overrightarrow{PD} \).

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