
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 if David's score on the national Mathematics Competition (which has 40 problems) was over 100, he could determine the exact number of problems David solved correctly. The scoring for this competition is slightly different: each correct answer gains 5 points, each wrong answer loses 1 point, and unanswered questions do not affect the score. Given that the score $s$ is calculated as $s = 40 + 5c - w$, if David's score had been any lower, but still above 100, John wouldn't have been able to determine the number of correctly solved problems. What was David's score?

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