
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
Given four non-overlapping points $P$, $A$, $B$, $C$ on a plane that satisfy $\overrightarrow{PA} + \overrightarrow{PB} + \overrightarrow{PC} = 0$ and $\overrightarrow{AB} + \overrightarrow{AC} = m \overrightarrow{AP}$, determine the value of the real number $m$.

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