
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
(I) Evaluate the expression $2\lg 5 + \lg 4 + \ln \sqrt {e}$;
(II) Given that the angle $\alpha$ in the second quadrant satisfies $\sin \alpha= \dfrac {1}{3}$, find the value of $\cos \alpha$;
(III) Given that $\tan \alpha=2$, find the value of $\dfrac {4\cos \alpha+\sin \alpha}{3\cos \alpha-2\sin \alpha}$.

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