
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
Luke guesses randomly on a 20-question multiple-choice test where each question offers four choices but only one is correct. Calculate the probability that Luke scores at least half the questions correct.

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