
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
(1) If the domain of $$y=\log_{\frac{1}{3}}(mx^{2}+2x+m)$$ is $\mathbb{R}$, find the range of the real number $m$;  
(2) When $x \in [-1, 1]$, find the minimum value $h(a)$ of the function $$y=\left(\left(\frac{1}{3}\right)^{x}\right)^{2}-2a\cdot \left(\frac{1}{3}\right)^{x}+3$$.

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