
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 sequence $\{a_n\}$ is an arithmetic sequence with the first term $a$ and common difference $1$, and $b_n = \frac{1+a_n}{a_n}$, if for any $n \in \mathbb{N}^*$, $b_n \geqslant b_8$ holds, then the range of values for the real number $a$ is ______.

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