
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 $A = \{x \mid -x^{2} + 2x + 15 \leqslant 0\}$, $B = \{x \mid |x-5| \lt 1\}$, find $A \cup B$, $(\complement _{R}A) \cap B$.

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