
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
On March 10, 2023, the "Implementation Opinions on Promoting the Development of New Energy Vehicle Industry in Chengdu" was officially issued. The opinion pointed out that in combination with the future charging demand of new energy vehicles, charging facilities should be built, and upgrades and renovations should be encouraged for existing parking spaces that do not currently have the conditions for construction. A certain shopping mall transformed some parking spaces into charging parking spaces, purchasing two types of charging piles, $A$ and $B$, at a cost of $50,000 and $80,000 respectively. It is known that the unit price of charging pile $A$ is $0.1$ million yuan higher than the unit price of charging pile $B$, and the quantity of charging pile $B$ purchased is twice the quantity of charging pile $A$. <br/>$(1)$ Find the unit prices of charging piles $A$ and $B$ respectively;<br/>$(2)$ The shopping mall conducted a survey and found that the existing transformed charging parking spaces cannot meet the charging needs of new energy vehicles. It was decided to purchase a total of 20 charging piles of types $A$ and $B$ with no more than $9.58$ million yuan. Find the maximum number of charging piles of type $A$ that can be purchased this time.

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