
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
Given ①{1,a}⊆{a^2-2a+2,a-1,0}, ②the solution set of the inequality 1＜ax+b≤3 with respect to x is {x|3＜x≤4}, ③the graph of the linear function y=ax+b passes through points A(-1,1) and B(2,7), choose one of the three conditions and complete the following question.

Question: Given _____, find the solution set of the inequality ax^2-5x+a＞0 with respect to x.

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