
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 $f(x)=\cos ^{2} \frac {x}{2}-\sin \frac {x}{2}\cos \frac {x}{2}- \frac {1}{2}$.
(1) Find the smallest positive period and the range of the function.
(2) Find the interval where the function is strictly decreasing.
(3) If $f(α)= \frac {3 \sqrt {2}}{10}$, find the value of $\sin 2α$.

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