
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 that \( \triangle ABC \) has a centroid \( G \), \( M \) is the midpoint of side \( BC \). A line through \( G \) parallel to \( BC \) intersects side \( AB \) at \( X \) and side \( AC \) at \( Y \). \( XC \) and \( GB \) intersect at point \( Q \), and \( YB \) and \( GC \) intersect at point \( P \). If the area of \( \triangle ABC \) is 32 square units, find the area of \( \triangle MPQ \).

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