
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 the inequality in terms of \\(x\\), \\(a{x}^{2}-3x+2\leqslant 0 \\), has the solution set \\(\left\{ \left.x \right|1\leqslant x\leqslant b\right\} \\).

  
\\((1)\\) Find the values of the real numbers \\(a\\) and \\(b\\);  
\\((2)\\) Solve the inequality: \\( \dfrac{x+3}{ax-b} > 0 \\).

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