
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 $f(x)=|2x-a|+a$, where $a \in \mathbb{R}$, and $g(x)=|2x-1|$.
(1) Let $a=2$, solve the inequality $f(x)+g(x)\leqslant 7$ with respect to $x$.
(2) If $f(x)\leqslant 6$ always holds when $g(x)\leqslant 5$, find the range of $a$.

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