
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
Simplify and compute:
$(1)$ Given $\tan \theta=2$, evaluate: $\dfrac {\sin (\theta+ \dfrac {\pi}{2})\cos ( \dfrac {\pi}{2}-\theta)-\cos ^{2}(\pi-\theta)}{1+\sin ^{2}\theta}$;
$(2)$ $\ln ( \sqrt {x^{2}+1}+x)+\ln ( \sqrt {x^{2}+1}-x)+\lg ^{2}2+(1+\lg 2) \cdot \lg 5-2\sin 30^{\circ}$.

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