
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 an arithmetic sequence {a<sub>n</sub>} that is an increasing sequence, and a<sub>1</sub> + a<sub>4</sub> = 0, a<sub>2</sub>a<sub>3</sub> = -1.
(1) Find the general term formula for the sequence {a<sub>n</sub>};
(2) Let b<sub>n</sub> = 3^{a<sub>n</sub> + 4}, and the sum of the first n terms of the sequence {b<sub>n</sub>} is T<sub>n</sub>. Does there exist a constant λ such that λT<sub>n</sub> - b<sub>n + 1</sub> is always constant? If it exists, find the value of λ; if not, explain the reason.

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