
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 $\dfrac{{\cos }^{2}\left(\alpha -\dfrac{\pi }{2}\right)}{\sin \left(\dfrac{5\pi }{2}+\alpha \right)\cdot \sin \left(\pi +\alpha \right)}=\dfrac{1}{2}$.

(Ⅰ) Find the value of $\tan \alpha$;

(Ⅱ) Find the value of $\sin 2\alpha +\cos 2\alpha$.

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