
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
David is taking a true/false exam with  $9$  questions. Unfortunately, he doesn’t know the answer to any of the questions, but he does know that exactly  $5$  of the answers are True. In accordance with this, David guesses the answers to all  $9$  questions, making sure that exactly  $5$  of his answers are True. What is the probability he answers at least  $5$  questions correctly?

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