
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 a "standard 01 sequence" {a_n} of 2m terms, where m=4, with m terms equal to 0 and m terms equal to 1, and for any k ≤ 2m, the number of 0's in {a_1, a_2, ..., a_k} is not less than the number of 1's, calculate the total number of different "standard 01 sequences".

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