
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
John tells Mary his score in the Australian Senior Mathematics Competition (ASMC), which was exactly 100. From this, Mary was able to determine the number of problems John solved correctly. If John's score had been over 95 but less than 100, Mary could not have determined this. What was John's score? (Recall that the ASMC consists of 25 multiple choice questions and that one's score, $s$, is computed by the formula $s = 25 + 5c - 2w$, where $c$ is the number of correct answers and $w$ is the number of wrong answers. Students are not penalized for problems left unanswered.)

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