
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
800 independent trials were conducted: in 200 of them, the probability of the expected outcome was 0.5, in 400 trials this probability was 0.4, and in the remaining cases, the probability of the favorable outcome was 0.3. Estimate from below the probability that the deviation in the frequency of the expected result from the average probability does not exceed 0.04 in absolute value.

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