
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 $f(x)=2\sin(2x+\varphi)$ where $|\varphi|<\frac{\pi}{2}$, the graph of $y=f(x)$ is shifted to the left by $\frac{\pi}{8}$ units, resulting in the function $y=g(x)$. If the graph of $g(x)$ is symmetric about the $y$-axis, find the minimum value of $g(x)+g(\frac{x}{2})$.

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