
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 $|2x+1|-|x-1|\leq\log_{2}a$ (where $a>0$).
(1) When $a=4$, find the solution set;
(2) If the inequality has solutions in $\mathbb{R}$, find the range of values for the real number $a$.

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