
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 $\{a_n\}$, the first three terms are $\lambda$, $6$, and $3\lambda$, respectively. The sum of the first $n$ terms is denoted as $S_n$, and $S_k = 165$.

1. Find the values of $\lambda$ and $k$.
2. Let $b_n = \frac{3}{2S_n}$, find the sum of the first $n$ terms of the sequence $\{b_n\}$, denoted as $T_n$.

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