
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 triangle \( ABC, \) \( E \) lies on \( \overline{AC} \) such that \( AE:EC = 3:2, \) and \( F \) lies on \( \overline{AB} \) such that \( AF:FB = 2:3. \) Let \( P \) be the intersection of \( \overline{BE} \) and \( \overline{CF}. \)
Determine the vector \( \overrightarrow{P} \) in the form \( x \overrightarrow{A} + y \overrightarrow{B} + z \overrightarrow{C}, \) where \( x, \) \( y, \) and \( z \) are constants such that \( x + y + z = 1. \)

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