
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
Find the solution set of the following inequalities:  
(1) Find the real number solutions for the inequality $$\frac {|x+1|}{|x+2|} \geq 1$$;  
(2) Solve the inequality $$\frac {a(x-1)}{x-2} > 1$$ with respect to $x$.

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