
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 that one of the symmetry centers of the function $f(x)=2\cos \left( \frac{πx}{3}+φ\right)$ is $(2,0)$, and $f(1) > f(3)$, determine the required transformation of the graph of the function $y=2\cos \frac{πx}{3}$.

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