
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 a function $y=a\sin x+b\cos x+c$, the graph has a maximum point at $(\dfrac{\pi}{4}, 4)$, and the minimum y-coordinate is $2$. If the graph is transformed such that the y-coordinate stays the same for every point, while the x-coordinate is reduced to half of its original size and then shifted left by $\dfrac{\pi}{8}$ units, we obtain the graph of $y=f(x)$. Find $f(\dfrac{2\pi}{3})$.

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