
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 knows that Alec got over 90 on the AHSME, from which he deduces the exact number of problems Alec solved correctly. Alec's score, if it had been any lower but still over 90, would not have allowed John to deduce the number correctly solved. Assuming the scoring system remains $s = 30 + 4c - w$, where $c$ is the number correct and $w$ is incorrect (no penalty for unanswered), how many problems did Alec get right?

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