
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  $x, y$  be positive real numbers. If \[129-x^2=195-y^2=xy,\] then  $x = \frac{m}{n}$  for relatively prime positive integers  $m, n$ . Find  $100m+n$ .

[i]Proposed by Michael Tang

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