
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
The function $f(x)=A\sin (ωx+α)(A > 0,ω > 0,-\frac {π}{2} < α < \frac {π}{2})$ has a minimum positive period of $π$, and $f(x)$ reaches its maximum value of $5$ at $x=\frac {π}{6}$.

(1) Find the analytic expression of $f(x)$ and its monotonically decreasing interval;

(2) After shifting the graph of the function $f(x)$ to the right by $m(m > 0)$ units, the graph of the function $y=g(x)$ is obtained, and $y=g(x)$ is an even function. Find the minimum value of $m$.

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