
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
An arithmetic sequence \(\{a_n\}\) satisfies \(a_1^2 + a_{10}^2 \leq 10\). Determine the range of values of \(S = a_{10} + a_{11} + \cdots + a_{19}\).

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