
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 $f(x)=4\cos(3x+\phi)(|\phi|<\frac{\pi}{2})$, its graph is symmetrical about the line $x=\frac{11\pi}{12}$. When $x_1,x_2\in(-\frac{7\pi}{12},-\frac{\pi}{12})$, $x_1\neq x_2$, and $f(x_1)=f(x_2)$, find $f(x_1+x_2)$.

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