
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 European Mathematics School is organizing a gathering for new students. The group of new students has less than $400$ members. When these students are arranged in columns of $17$, $16$ people are left in the last column. When they line up in columns of $19$, $12$ people are in the last column. Determine the total number of new students.

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