
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
Bob told Alice his score on a customized mathematics examination, which was over 100. From this, Alice was able to determine the number of problems Bob solved correctly. If Bob's score had been any lower, but still over 100, Alice could not have determined this. What was Bob's score? The examination consists of 50 multiple-choice problems and one's score, \( s \), is computed by the formula \( s = 50 + 5c - 2w \), where \( c \) is the number of correct answers and \( w \) is the number of wrong answers. (Students are not penalized for problems left unanswered.)

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