
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 $f(x) = \cos(2x - \frac{\pi}{3}) + \sin^2x - \cos^2x$.
(Ⅰ) Find the smallest positive period of the function $f(x)$ and the equation of the axis of symmetry for the graph;
(Ⅱ) Let the function $g(x) = f(x)^2 + f(x)$, determine the range of $g(x)$.

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