
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
Which of the following statements is correct?
$①$ For any $x \in \mathbb{R}$, it holds that $3^{x} > 2^{x}$;
$②$ If $a > 0$ and $a \neq 1$, $M > 0$, $N > 0$, then $\log_{a}(M+N) = \log_{a}M \cdot \log_{a}N$;
$③$ The maximum value of $y = \left( \frac{1}{2} \right)^{|x|}$ is $1$;
$④$ In the same coordinate system, the graphs of $y = 2^{x}$ and $y = \left( \frac{1}{2} \right)^{x}$ are symmetric about the $y$-axis.

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