
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 $f(x)=\sin x+\lambda\cos x (\lambda\in\mathbb{R})$ is symmetric about $x=-\frac{\pi}{4}$, find the equation of one of the axes of symmetry of function $g(x)$ obtained by expanding the horizontal coordinate of each point of the graph of $f(x)$ by a factor of $2$ and then shifting it right by $\frac{\pi}{3}$.

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