
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]


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Given $f(x)=\sin (x+ \frac {π}{2})$ and $g(x)=\cos (x- \frac {π}{2})$, determine the correct conclusion(s) from the options below.

(1) The smallest positive period of the function $y=f(x) \cdot g(x)$ is $π$.

(2) The maximum value of the function $y=f(x) \cdot g(x)$ is $\frac {1}{2}$.

(3) The graph of the function $y=f(x) \cdot g(x)$ is symmetric about the point $(\frac {π}{4},0)$.

(4) Translating the graph of function $f(x)$ to the right by $\frac {π}{2}$ units results in the graph of function $g(x)$.

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