
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
In the frequency distribution histogram of a sample, there are a total of 9 small rectangles. If the area of the first rectangle is 0.02, the areas of the first five and the last five rectangles respectively form arithmetic sequences with common differences that are opposite in sign. If the sample size is 1600, then the frequency of the middle group (i.e., the fifth group) is ▲.

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