
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 $f(x)=\sin \left(x- \frac {\pi}{6}\right)+\cos \left(x- \frac {\pi}{3}\right)$, $g(x)=2\sin ^{2} \frac {x}{2}$.  
(Ⅰ) If $\alpha$ is an angle in the first quadrant, and $f(\alpha)= \frac {3 \sqrt {3}}{5}$, find the value of $g(\alpha)$.  
(Ⅱ) Find the set of values of $x$ for which $f(x)\geqslant g(x)$ holds.

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