
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 $w > 0$, the graph of the function $y=2\cos \left(wx+ \dfrac {\pi}{7}\right)-1$ coincides with its original position after being translated $\dfrac {4\pi}{3}$ units to the right. Determine the minimum value of $w$.

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