
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 curve $f(x)=\frac{2}{3}{x}^{3}$, find the value of $\frac{{\mathrm{sin}}^{2}\alpha -{\mathrm{cos}}^{2}\alpha }{2\mathrm{sin}\alpha \mathrm{cos}\alpha +{\mathrm{cos}}^{2}\alpha }$, where $\alpha$ is the angle of inclination of the tangent line at the point $(1,f(1))$.

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