
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
In the sequence $\\{a_n\\}$, let $S_n$ denote the sum of the first $n$ terms, and $S_n = 1 + ka_n$ $(k \neq 0, k \neq 1)$.

(1) Find $a_n$;

(2) When $k=-1$, find the value of ${a_1}^2 + {a_2}^2 + \cdots + {a_n}^2$.

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