
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 Eastern Mathematics Institute is welcoming its new batch of students. There are fewer than 600 students in the new batch. When the students are arranged in columns of $25$, there are $24$ students in the last column. When they are arranged in columns of $19$, there are $15$ students in the last column. Determine the number of students in the new batch.

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