
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
In the geometric sequence $\left\{ a_n \right\}$, $a_4=8$ and the common ratio $q=2$. If the inequality $\frac{\lambda^2}{3}-\lambda \geqslant \frac{1}{a_1^2}+\frac{1}{a_2^2}+\frac{1}{a_3^2}+\cdots +\frac{1}{a_n^2}$ holds for any $n\in \mathbb{N}^*$, then the range of the real number $\lambda$ is.

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