
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 deduced the exact number of problems that Mary solved correctly on the AHSME after she mentioned that her score was over 90. If her score had been any lower, but still over 90, John would not have been able to determine the number of problems she solved correctly. What was Mary’s score? Assume the scoring formula is now \( s = 35 + 5c - w \), where \( c \) is the number of correct answers and \( w \) is the number of wrong answers. There are still 30 problems in total.

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