
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
Let the sequence {$\frac{1}{a_n}$} be a geometric sequence, and let $S_n$ be the sum of the first $n$ terms of the sequence {$a_n$}. Given that $a_1 = 1$ and $a_2 \cdot a_3 \cdot a_4 = 64$,  
(1) Find the general term of the sequence {$a_n$};  
(2) When the sequence {$S_n+\lambda$} is also a geometric sequence, find the value of $\lambda$.

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