
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
Determine the highest possible score Mary could have received on the AHSME if John could uniquely identify the number of problems she solved correctly, given her score was over 100 and under certain conditions. The AHSME scoring system is \( s = 30 + 4c - w \), and there are 30 multiple choice questions.

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