
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 set $A=\{x| \frac {(x+1)^{2}(2-x)}{4+x}\geq0\}$, and the set $B=\{x| (x-a)(x-2a+1)\leq0\}$  
(1) Find the set $A$;  
(2) If $A\cup B=A$, find the range of the real number $a$.

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