
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 $f(x)=(\log_{3}x)^{2}+(a-1)\log_{3}x+3a-2$ where $x > 0$ and $a \in \mathbb{R}$.

(1) If the range of the function $f(x)$ is $[2,+\infty)$, find the value of $a$.

(2) If $f(3x)+\log_{3}(9x) \leqslant 0$ holds for any $x \in [3,9]$, find the range of values for $a$.

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