
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 the real numbers \(a_{1}, a_{2}, \cdots, a_{5}\) satisfying
$$
\sum_{i=1}^{5} a_{i}^{2} = 1,
$$
find the maximum value of 
$$
T=\sum_{i=1}^{5}\left|a_{i}-a_{i+1}\right|
$$
where \(a_{6} = a_{1}\).

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