
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 universal set $U = \mathbb{R}$, set $A = \{x \in \mathbb{R} | -5 \leq 3x - 2 \leq 1\}$, set $B = \{x \in \mathbb{R} | \log_{2}(2-x) \leq 1\}$.  
$(1)$ Find $A \cap B$ and $A \cup B$.  
$(2)$ Find $(\complement_{\mathbb{R}}B) \cup A$.

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