
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 positive real number, and let $y = f(x)$ be an odd function defined on $\mathbb{R}$. When $x < 0$, $f(x) = x + \frac{a}{x} + 7$. If $f(x) \geq 1 - a$ holds true for any $x \geq 0$, then the range of values for the real number $a$ is _______.

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