
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 \( a \) does the equation

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

have exactly one solution?

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