
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
(1) Given the function $f(x)=2x+2\sin x+\cos x$, the slope of the tangent line at the point $(α,f(α))$ is 2. Find the value of $\frac{\sin (π-α)+\cos (-α)}{2\cos (\frac{π}{2}-α)+\cos (2π-α)}$.
(2) In triangle $△ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. Given $a=1$ and $a\cos C+\frac{1}{2}c=b$, find the range of values for the perimeter $l$ of $△ABC$.

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