
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 $\{a_n\}$ is given, where $a_1 < a_2 < a_3 < \ldots < a_n$ and $a_3$, $a_6$ are the two real roots of the quadratic equation $x^2 - 10x + 16 = 0$.
(1) Find the general formula for the sequence $\{a_n\}$.
(2) Determine whether 268 is a term in this sequence. If so, identify which term it is; if not, explain why.

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