
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
Let \( n \geq 3 \) and \( a_1, \ldots, a_n \) be real numbers such that \( \sum a_i^2 = 1 \). Find the maximum value of 

$$
\sum_{i=2}^{n+1} \left| a_i - a_{i-1} \right|.
$$

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