
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 sets $A=\{x|2^{4x+6}\geqslant 64^{x}\}$ and $B=\{x|2x^{2}+x-15\leqslant 0}$. Find the sets $A$ and $(\complement _{R}A)\cup B$. Also, given set $C=\left\{{x|-2≤x-k≤\frac{1}{2}}\right\}$, if $C\subseteq B$, find the range of real number $k$.

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