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

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