
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 $UVW$ be a right triangle in the xy-plane with a right angle at $W$. Given that the length of the hypotenuse $UV$ is $26$, and that the medians through $U$ and $V$ lie along the lines $y=x-1$ and $y=2x$ respectively, find the area of triangle $UVW$.

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