
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 evaluate:
(1) Calculate the value of $\frac {1}{\log_{4}6}+6^{\log_{6} \sqrt {3}-1}-2\log_{6} \frac {1}{3}$;
(2) Given $\tan\alpha=2$ and $\sin\alpha+\cos\alpha < 0$, find the value of $\frac {\tan(\pi-\alpha)\cdot \sin(-\alpha+ \frac {3\pi}{2})}{\cos(\pi +\alpha )\cdot \sin(-\pi -\alpha )}$.

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