
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 function $f(x)=|2x-1|$, where $x\in R$.
(1) If the solution set of the inequality $f(x)\leqslant a$ is $\{x|0\leqslant x\leqslant 1\}$, find the value of $a$.
(2) If the domain of $g(x)= \frac {1}{f(x)+f(x+1)+m}$ is $R$, find the range of values for the real number $m$.

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