
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 $f(x)=|2x-a|+a$, where $a\in R$, and $g(x)=|2x-1|$.
(I) If $g(x)\leqslant 5$ always implies $f(x)\leqslant 6$, find the maximum value of $a$.
(II) If $f(x)+g(x)\geqslant 3$ for all $x\in R$, find the range of possible values for $a$.

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