
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 $f(x)= \sqrt {3}\cos \left( \frac {\pi}{2}-2x\right)+2\cos ^{2}x-1$  
$(1)$ Find the smallest positive period of the function $f(x)$ and its intervals of monotonic decrease;  
$(2)$ Shift the graph of $f(x)$ to the left by $\frac {\pi}{12}$ units and then upward by $1$ unit to obtain the graph of $g(x)$. Determine the range of $g(x)$ in the interval $\left[0, \frac {\pi}{2}\right]$.

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