
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 $f(x) = (\log_3{x})^2 + (a-1)\log_3{x} + 3a - 2$ for $x > 0$ and $a \in \mathbb{R}$.
1. If the range of function $f(x)$ is $[2, +\infty)$, find the value of $a$.
2. If $f(3x) + \log_3(9x) \leq 0$ holds true for any $x \in [3, 9]$, determine the range of values of $a$.

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