
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
Given Dave presses the up or down button randomly from each floor of the elevator at Dave's Amazing Hotel, calculate the probability that he is on the first floor after doing this 482 times.

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