
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 radius of the inscribed circle in a triangle is \(\frac{4}{3}\), and the lengths of the heights of the triangle are whole numbers whose sum is 13. Calculate the lengths of the sides of the triangle.

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