
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
The National University’s Math Department is arranging a group activity for their new batch which contains fewer than $400$ students. When the students are arranged in columns of $17$, $15$ are in the last column. When the students arrange themselves in columns of $19$, there are $10$ students in the last column. Determine the total number of students in this new batch.

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