
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 the sequence $\{a_n\}$ with the general term $a_n = 3^n$, let the sum of the first $n$ terms of $\{a_n\}$ be $S_n$, if there exists $n \in \mathbb{N}^*$ such that $(S_{n}+ \frac {3}{2})k \geqslant 3n-6$ holds, then the range of values for the real number $k$ is ____.

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