
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-angled triangle in the $xy$ plane, with $C$ as the right angle. The hypotenuse $AB$ has a length of 60. The medians drawn from points $A$ and $B$ lie on 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}
user