
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 $\tan \alpha=3$, compute:
$(1) \dfrac {4\sin \alpha-2\cos \alpha}{5\cos \alpha +3\sin \alpha }$
$(2)1-4\sin \alpha\cos \alpha+2\cos ^{2}\alpha.$

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