
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 triangle  $ABC$  be a right triangle in the xy-plane with a right angle at  $C$ . Given that the length of the hypotenuse  $AB$  is 60, and that the medians through  $A$  and  $B$  lie along the lines  $y=x+3$  and  $y=2x+4$  respectively, find the area of triangle  $ABC$ .

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