
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
On a modified version of the American High School Mathematics Examination (AHSME), which consists of 30 multiple-choice questions, a student's score \( s \) is now computed by the formula \( s = 30 + 5c - 2w - n \), where \( c \), \( w \), and \( n \) are the numbers of correct answers, wrong answers, and questions left unanswered, respectively. Sara tells her friend Liam her score, which was exactly \(90\). From this information alone, Liam was able to deduce the number of problems Sara solved correctly. If Sara's score had been any lower, but still over \(85\), Liam could not have determined this. How many problems did Sara solve correctly?

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