
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
An $n$-bit check code is a digital transmission unit consisting of $n$ "$0$"s or "$1$"s, divided into odd parity check code and even parity check code. If a check code contains an odd number of "$1$"s, it is called an odd parity check code. Determine the number of odd parity check codes in a $6$-bit check code.

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