
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
(1) Given $\tan \theta=2$, find the value of $\dfrac {\sin (\theta-6\pi)+\sin ( \dfrac {\pi}{2}-\theta)}{2\sin (\pi+\theta)+\cos (-\theta)}$;
(2) Given $-\dfrac {\pi}{2} < x < \dfrac {\pi}{2}$, and $\sin x+\cos x= \dfrac {1}{5}$, find the value of $\tan x$.

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