
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 $ABC$, vertex $B$ is connected to the point that divides side $AC$ into thirds, closer to $A$. The intersection of this segment and the median from $A$ is denoted as $P$, and the centroid of the triangle as $S$. In what ratio does $P$ divide the segment $AS$?

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