
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
In an election, there are two candidates, A and B, who each have 5 supporters. Each supporter, independent of other supporters, has a \(\frac{1}{2}\) probability of voting for his or her candidate and a \(\frac{1}{2}\) probability of being lazy and not voting. What is the probability of a tie (which includes the case in which no one votes)?

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