
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 that $a > 0$, the function $f(x)=-2a\sin (2x+ \frac {π}{6})+2a+b$ is such that $-5\leqslant f(x)\leqslant 1$ when $x\in[0, \frac {π}{2}]$.

1. Let $g(x)=f(x+ \frac {π}{2})$, and $\lg g(x) > 0$, find the monotonically increasing interval of $g(x)$.
2. If the inequality $|f(x)-m| < 3$ holds for any $x\in(0, \frac {π}{6}]$, find the range of values for the real number $m$.

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