
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
Xiao Zhang participated in a test with ten multiple-choice questions. Each correct answer earns one point, each wrong answer deducts one point, and no answer earns zero points. His goal is to score at least 7 points to pass. Xiao Zhang is certain that he answered the first six questions correctly. Each of the remaining questions has a probability of $\frac{1}{2}$ of being correct. How many questions should Xiao Zhang attempt to maximize his probability of passing?

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