
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 $f(x)=\sin (x- \frac {π}{6})+ \frac {1}{2}$.
(1) If $x\in[0, \frac {π}{2}]$, $f(x)= \frac {11}{10}$, find the value of $\cos x$;
(2) In $\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively, and satisfy $2b\cos A\leqslant 2c- \sqrt {3}a$, find the range of $f(B)$.

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