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

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