
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
Let $a$ be a real constant, and $y=f(x)$ be an odd function defined on $\mathbb{R}$. When $x < 0$, $f(x)=9x+\frac{{{a}^{2}}}{x}+7$. If $f(x)\geqslant a+1$ holds for all $x\geqslant 0$, find the range of $a$ values.

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