
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
A direct measurement found that the diameter of a circle is 6.4 cm, with a maximum error not exceeding $0.05 \mathrm{~cm}$. Find the approximate maximum error in estimating the area, calculated by the formula $S=\frac{1}{4} \pi x^{2}$ (where $x$ is the diameter).

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