
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
At the entrance exam in mathematics, 15% of the candidates did not solve any problems, 144 people solved the problems with errors, and the number of people who solved all the problems correctly is in the ratio of 5 to 3 to those who did not solve any at all. How many people took the mathematics exam on that day?

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