
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
The sides  $x$  and  $y$  of a scalene triangle satisfy  $x + \frac{2\Delta }{x}=y+ \frac{2\Delta }{y}$  , where  $\Delta$  is the area of the triangle. If  $x = 60, y = 63$ , what is the length of the largest side of the triangle?

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