
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
Triangles \( PQR \) and \( PST \) have areas \( 645 \) and \( 2580, \) respectively, with \( Q = (0,0), R = (93, 0), S = (200, 200), \) and \( T = (209, 209). \) What is the sum of all possible \( x \)-coordinates of \( P \)?

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