
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
Juan needs to calculate the area of a circle based on his measurements. The actual diameter of the circle is 30 cm, and Juan's measurement error for the diameter is up to $15\%$. He also measures the radius directly and could make an error of up to $10\%$. What is the largest possible percent error, in percent, in Juan's computed area of the circle based on these measurements?

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