
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 $\tan \alpha=3$, find the values of:

$(1)\ \dfrac{3\sin \alpha +2\cos \alpha }{\sin \alpha -4\cos \alpha } \quad\quad\quad\quad (2)\ \dfrac{5{{\cos }^{2}}\alpha -3{{\sin }^{2}}\alpha }{1+{{\sin }^{2}}\alpha }$

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