
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
The sequence $\left\{a_{n}\right\}$ is defined by $a_{1}=1$ and $a_{n+1}=\sqrt{a_{n}^{2}-2a_{n}+3}+c$ for $n \in \mathbf{N}^{*}$, where $c$ is a constant greater than 0.

(1) If $c=1$, find the general term of the sequence $\left\{a_{n}\right\}$.

(2) If the sequence $\left\{a_{n}\right\}$ is bounded above, find the range of values for $c$.

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