
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
Find the probability that a randomly selected 8-digit number composed of 0s and 1s has the sum of the digits in even positions equal to the sum of the digits in odd positions.

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