
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 $f(x)=a+b\cos x+c\sin x$ whose graph passes through points $A(0,1)$ and $B(\frac{\pi}{2},1)$.
(1) Given $b > 0$, find the interval(s) where $f(x)$ is monotonically decreasing;
(2) Given $x\in(0,\frac{\pi}{2})$ and $|f(x)|\leqslant 2$ always holds true, find the range of values for the real number $a$.

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