
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
Mary told John her score on the American High School Mathematics Examination (AHSME), which was over 80.  From this, John was able to determine the number of problems Mary solved correctly.  If Mary's score had been any lower, but still over 80, John could not have determined this.  What was Mary's score?  (Recall that the AHSME consists of 30 multiple-choice problems and that one's score,  $s$ , is computed by the formula  $s = 30 + 4c - w$ , where  $c$  is the number of correct 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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