
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 American Mathematics College welcomes its incoming freshman class, which totals fewer than $500$ people. When the freshmen are requested to line up in columns of $25$, $24$ are left in the last column. When the freshmen are asked to form columns of $19$, $11$ remain in the last column. Determine the total number of people in the incoming freshman class.

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