
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
For which values of the parameter \( a \), the equation

\[
3^{x^{2}+6 a x+9 a^{2}} = a x^{2}+6 a^{2} x+9 a^{3}+a^{2}-4 a+4
\]

has exactly one solution?

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