
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
There are two types of products, $A$ and $B$. Product $A$ costs $20$ yuan each, and product $B$ costs $50 yuan each. Xiao Liang plans to buy a total of $10$ items of products $A$ and $B$, with a total cost not exceeding $350$ yuan. How many items of product $A$ should he buy at least?

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