
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
Let \( ABC \) be a triangle, \( M \) be the midpoint of \( BC \), and \( N \) be one-third of the way along \( AC \) starting from \( C \). The line \( MN \) intersects \( AB \) at \( P \). Determine the position of \( P \) relative to \( A \) and \( B \).

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