
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 $(tan⁡α−3)(sin⁡α+cos⁡α+3)=0$, find the value of:
$(1) \frac{4sin⁡α+2cos⁡α}{5cos⁡α+3sin⁡α}$
$(2) 2+\frac{2}{3}sin^2α+\frac{1}{4}cos^2α$

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