
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
An equilateral triangle \( ABC \) has side length \( 2 \sqrt{3} \). Two moving points \( P \) and \( M \) in the same plane as \( ABC \) satisfy \( |\overrightarrow{AP}| = 1 \) and \(\overrightarrow{PM} = \overrightarrow{MB} \). What is the minimum value of \( |\overrightarrow{CM}| \)?

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