
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 $f(x)=4\cos (\omega x+\varphi)$ ($\omega > 0$, $0 < \varphi < \pi$) is an odd function, $A(a,0)$, $B(b,0)$ are two points on its graph. If the minimum value of $|a-b|$ is $1$, evaluate $f\left( \dfrac{1}{6} \right)$.

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