
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 April, all the fragrant flowers on earth have withered, while the peach blossoms in the mountain temple are just beginning to bloom." To experience nature and depict its beauty, Xiaoming and his classmates plan to purchase a certain number of brushes and canvases for sketching. It is known that purchasing $2$ boxes of brushes and $4$ canvases costs a total of $94$ yuan, and purchasing $4$ boxes of brushes and $2$ canvases costs a total of $98$ yuan. <br/>$(1)$ How much does it cost to purchase one box of brushes and one canvas each? <br/>$(2)$ Xiaoming and his classmates discuss that the total number of boxes of brushes and canvases should be $10$, and the total cost of purchasing these sketching tools should not exceed $157$ yuan. What is the minimum number of canvases to purchase? <br/>$(3)$ Under the conditions of $(2)$, if at most $8$ canvases are needed, which purchasing plan is more cost-effective?

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