
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 $f(x)=2 \sqrt {3}\sin (x+ \frac {π}{4})\cos (x+ \frac {π}{4})+\sin 2x+a$ with a maximum value of $1$.

(1) Find the interval where the function $f(x)$ is monotonically increasing.
(2) Translate the graph of $f(x)$ to the left by $\frac {π}{6}$ units to obtain the graph of $g(x)$. Find the range of real values $m$ for which the equation $g(x)=m$ has a solution in the interval $x\in[0, \frac {π}{2}]$.

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