
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 power function $y=x^{3m-9}$, where $m\in \mathbb{N}^*$, the graph of the function is symmetric about the $y$-axis, and the function value decreases as $x$ increases in the interval $(0,+\infty)$. Find the range of real numbers $a$ that satisfy ${{(a+1)}^{\frac{m}{3}}} < {{(3-2a)}^{\frac{m}{3}}}$.

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