
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 functions $f(x)=2\sin \left(\pi x+\frac{\pi }{3}\right)$ and $g(x)=2\cos \left(\pi x+\frac{\pi }{3}\right)$, find the area of the triangle formed by the intersection points of the two functions within the interval $\left[-\frac{4}{3},\frac{7}{6}\right]$.

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