
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 $f(x) = x^{9-3m}$ $(m \in N^*)$ whose graph is symmetric about the origin and is monotonically increasing on $\mathbb{R}$.

$(1)$ Find the expression for $f(x)$;  
$(2)$ Find the range of values for $a$ that satisfies $f(a+1) + f(3a-4) < 0$.

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