
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 $f(x)=\cos{x}\sin\left(x+\frac{\pi}{3}\right)-\sqrt{3}\cos^2{x}+\frac{\sqrt{3}}{4}-1$ where $x\in \mathbb{R}$. Find:

1. The smallest positive period of $f(x)$ and the equation of the axis of symmetry.
2. The maximum and minimum values of $f(x)$ on the interval $[-\frac{\pi}{4}, \frac{\pi}{4}]$, and write down the corresponding values of $x$.

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