
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 $f(x)=2\sin^{4}x+2\cos^{4}x+\cos^{2}2x-3$.

(1) Find the smallest positive period, the equations of the axes of symmetry, and the intervals of monotonic decrease for the function $f(x)$.

(2) Given that the graph of the function $f(x)$ is transformed such that every point's vertical coordinate remains unchanged, and the horizontal coordinate is stretched to twice its original length, then the entire graph is shifted to the left by $\frac{\pi}{6}$ units to obtain the graph of the function $g(x)$. When $x \in \left[-\frac{\pi}{4}, \frac{\pi}{6}\right]$, find the minimum value of the function $g(x)$ and the value of $x$ for which this minimum is attained.

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