
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 pyramid \( SABC \), all faces are equilateral triangles; point \( M \) is the centroid of triangle \( ABC \), and point \( P \) is the midpoint of the edge \( SC \). Find the decomposition of vector \( \overrightarrow{MP} \) in terms of vectors \( \overrightarrow{AB} \), \( \overrightarrow{AC} \), and \( \overrightarrow{AS} \).

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