
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 $m(m\geqslant 3)$ rectangles, and the sum of the areas of the first $3$ groups of rectangles is equal to $\frac{1}{4}$ of the sum of the areas of the remaining $m-3$ rectangles. The sample size is $120$. If the areas of the first $3$ groups of rectangles, $S_1, S_2, S_3$, form an arithmetic sequence and $S_1=\frac{1}{20}$, then the frequency of the third group is ______.

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