
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 a modified version of the American High School Mathematics Examination (AHSME), the scoring formula has been changed to $s = 30 + 4c - 2w$, where $s$ is the score, $c$ the number of correct answers, and $w$ the number of wrong answers, with no penalties for unanswered questions. Mary told John that her score was over $100$. From this information alone, John was able to determine the number of problems Mary solved correctly. If Mary's score had been any lower, but still over $100$, John would not have been able to determine this. What was Mary's score?

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