
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
During a sports festival, the student union of Experiment High School organized a "charity sale" activity, preparing a total of $100$ notebooks and sticky notes as two types of cultural and creative products. If $3$ notebooks and $2$ sticky notes are sold, the income is $65$ yuan, and if $4$ notebooks and $3$ sticky notes are sold, the income is $90$ yuan. <br/>$(1)$ Find the selling price of notebooks and sticky notes respectively; <br/>$(2)$ Given that the number of notebooks does not exceed $3$ times the number of sticky notes, determine the quantities of notebooks and sticky notes that will maximize the total income, and find the maximum total income.

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