
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
If the graph of the function $f(x)= a+b\cos x+c\sin x$ passes through points $A(0,1)$ and $B\left( \dfrac{\pi}{2},1 \right)$, and $|f(x)|\leq 2$ always holds when $x\in\left[0, \dfrac{\pi}{2}\right]$, then the range of the real number $a$ is ______________.

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