
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 $f(x)=|x-a|$, where $a > 1$.

(1) When $a=3$, find the solution set of the inequality $f(x)\geqslant 4-|x-4|$.

(2) If the area of the triangle formed by the graph of the function $h(x)=f(2x+a)-2f(x)$ and the $x$ and $y$ axes is greater than $a+4$, find the range of values for $a$.

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