
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 $f(x)=2\sin (2x- \frac {π}{6})+a$, where $a$ is a constant,
(1) Find the minimum positive period and the interval where the function is strictly increasing;
(2) If the minimum value of $f(x)$ on the interval $[0, \frac {π}{2}]$ is $3$, find the value of $a$;
(3) If the graph of function $f(x)$ is shifted to the left by $m(m > 0)$ units to obtain the graph of function $g(x)$, and the graph of $g(x)$ is symmetric about the $y$-axis, find the minimum value of the real number $m$.

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