
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
(1) Given that $\cos\left(\frac{\pi}{4} + x\right) = \frac{3}{5}$, where $\frac{17\pi}{12} < x < \frac{7\pi}{4}$, find the value of $\frac{\sin{2x} + 2\sin^2{x}}{1 - \tan{x}}$.
(2) Let $\vec{e}_1$ and $\vec{e}_2$ be two unit vectors with an angle of 60° between them. Find the angle between vectors $\vec{a} = 2\vec{e}_1 + \vec{e}_2$ and $\vec{b} = -3\vec{e}_1 + 2\vec{e}_2$.

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