
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
Define a "standard 01 sequence" $\{a_n\}$ as follows: $\{a_n\}$ has $2m$ terms, among which $m$ terms are $0$ and $m$ terms are $1$, and for any $k \leqslant 2m$, the number of $0$s among $a_1, a_2, \ldots a_k$ is not less than the number of $1$s. If $m=4$, calculate the total number of different "standard 01 sequences".

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