
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 function $f(x)=\left( \frac{1}{3} \right)^{ax^{2}-4x+3}$.

$(1)$ If $a=-1$, find the intervals of monotonicity for $f(x)$;

$(2)$ If $f(x)$ has a maximum value of $3$, find the value of $a$.

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