
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 participated in a modified version of the American High School Mathematics Examination (AHSME), which now consists of $35$ multiple-choice problems. She told John her score, which was over $90$. Using the new scoring system, where a student’s score $s$ is given by $s=35+4c-w$, where $c$ is the number of correct answers and $w$ is the number of wrong answers (no penalty for unanswered questions), John was able to determine exactly how many problems Mary solved correctly. If Mary's score had been any lower, but still over $90$, John wouldn't have been able to determine this. What was Mary's score?

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