
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
At the end of January 2023, the artificial intelligence chat program named "$ChatGTP$" created by Elon Musk, Peter Thiel, and others from the artificial intelligence research company $openAI$ entered China and quickly attracted domestic attention with its extremely high level of intelligence. Deep learning is a representative implementation method of artificial intelligence, which is based on neural networks. In neural network optimization, the exponential decay learning rate model is $L=L_0D^{\frac{G}{G_0}}$, where $L$ represents the learning rate used in each optimization round, $L_{0}$ represents the initial learning rate, $D$ represents the decay factor, $G$ represents the training iteration rounds, and $G_{0}$ represents the decay rate. It is known that the initial learning rate of a certain exponential decay learning rate model is $0.5$, the decay rate is $18$, and when the training iteration rounds are $18$, the learning rate decays to $0.4$. The minimum number of training iteration rounds required for the learning rate to decay to below $0.2$ (excluding $0.2$) is ______. (Reference data: $\lg 2\approx 0.3010$)

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