
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 sets $M={x|-2x+1\geqslant 0}$ and $N={x|x < a}$, if $M\subseteq N$, determine the range of $a$.

A) $a > \dfrac{1}{2}$

B) $a < \dfrac{{1}}{{2}}$

C) $a\leqslant \dfrac{{1}}{{2}}$

D) $a\geqslant \dfrac{{1}}{{2}}$

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