
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
How many times do we need to flip a coin so that with an error probability of less than 0.01, we can state that the frequency of getting heads will be between 0.4 and 0.6?

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