
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 $f(x)=4\sin (2x+φ)$, with the condition $|φ| < \dfrac {π}{2}$, its graph is symmetric about the line $x= \dfrac {π}{12}$. When $x\_1$, $x\_2 ∈(- \dfrac {7π}{6},- \dfrac {5π}{12})$, $x\_1\neq x\_2$, and $f(x\_1)=f(x\_2)$, find the value of $f(x\_1+x\_2)$.

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