
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 a sequence $\{a_n\}$ that satisfies $a_1 = -\frac{6}{7}$, and $1 + a_1 + a_2 + \ldots + a_n - \lambda a_{n+1} = 0$ ($\lambda \neq 0$, $\lambda \neq -1$, $n \in \mathbb{N}^*$):
1. Find the general term formula for $a_n$.
2. When $\lambda = \frac{1}{3}$, determine if there are any three terms in the sequence $\{a_n\}$ that form an arithmetic sequence. If so, find them; if not, provide a reason.

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