
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 problem is to determine the error bound for the construction of a central angle associated with the side of a regular 18-sided polygon (with a $20^\circ$ central angle) using a 4-digit trigonometric table. The goal is to find out how accurate this angle can be made when only a 4-digit function table is available for calculations. A rational number's square root can be determined to any desired precision without the use of tables.

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