
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]


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The Global School of Mathematics is organizing a gathering for new students. The total number of new students is less than $600$. When students are arranged in lines of $28$, there remain $27$ students in the last row. Additionally, when they are arranged in lines of $26$, there remain $20$ students in the last row. Determine the total number of new students at the gathering.

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