
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
A sequence \(\{a_n\}\) consists of 11 terms, where \(a_1=0\), \(a_{11}=4\), and the absolute difference between consecutive terms is 1, that is \(|a_{k+1} - a_k|=1\) for \(k=1,2,\ldots,10\). Calculate the number of different sequences \(\{a_n\}\) that satisfy these conditions.

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