
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
In a right triangle $ABC$, there is a rectangle $ADKM$ such that its side $AD$ lies on the leg $AB$, its side $AM$ lies on the leg $AC$, and the vertex $K$ is on the hypotenuse $BC$. The leg $AB$ is equal to 5 and the leg $AC$ is equal to 12. Find the sides of the rectangle $ADKM$ if its area is $40/3$ and its diagonal is less than 8.

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