
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 sequence $\left\{a_{n}\right\}$ with 100 terms, where $a_{1}=0$ and $a_{100}=475$, and $\left|a_{k+1}-a_{k}\right|=5$ for $k=1,2,\cdots, 99$, determine the number of different sequences that satisfy these conditions.

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