
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
Let \\(f(x)=2\sin (180^{\circ}-x)+\cos (-x)-\sin (450^{\circ}-x)+\cos (90^{\circ}+x)\\).
\\((1)\\) If \\(f(\alpha)= \dfrac {2}{3}\cdot\alpha\in(0^{\circ},180^{\circ})\\), find \\(\tan \alpha\\);
\\((2)\\) If \\(f(\alpha)=2\sin \alpha-\cos \alpha+ \dfrac {3}{4}\\), find the value of \\(\sin \alpha\cdot\cos \alpha\\).

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