
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

In the exam, there were 25 problems of three types: easy ones worth 2 points each, medium ones worth 3 points each, and hard ones worth 5 points each. Correctly solved problems were rewarded with the specified points based on difficulty; otherwise, they received 0 points. The best possible total score on the exam was 84 points. Peter correctly solved all the easy problems, half of the medium problems, and one-third of the hard problems.

How many points did Peter score on his exam?

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