
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 $f(x)=\sin (2x+φ)+2\sin ^{2}x (|φ| < \dfrac {π}{2})$ whose graph passes through the point $(\dfrac {π}{6}, \dfrac {3}{2})$.
(1) Find the minimum value of the function $f(x)$ on $[0, \dfrac {π}{2}]$;
(2) Let $C$ be an acute angle, and the lengths of the sides opposite to the internal angles $A$, $B$, $C$ of $\triangle ABC$ are $a$, $b$, $c$ respectively. If $x=C$ is a symmetric axis of the curve $y=f(x)$, and the area of $\triangle ABC$ is $2 \sqrt {3}$, $a+b=6$, find the length of side $c$.

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