
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
Consider the sequence \(\{a_{n}\}\) with 100 terms, where \(a_{1} = 0\) and \(a_{100} = 475\). Additionally, \(|a_{k+1} - a_{k}| = 5\) for \(k = 1, 2, \cdots, 99\). How many different sequences satisfy these conditions?

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