
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 $\cos (\frac{π}{4}+x)= \frac{3}{5}$ and $\frac{17π}{12} < x < \frac{7π}{4}$, find the value of $\frac{\sin 2x+2\sin ^{2}x}{1-\tan x}$.
(2) If $\overrightarrow{e_{1}}$ and $\overrightarrow{e_{2}}$ are two unit vectors with an angle of $60^{\circ}$ between them, find the angle between $\overrightarrow{a}=2 \overrightarrow{e_{1}}+ \overrightarrow{e_{2}}$ and $\overrightarrow{b}=-3 \overrightarrow{e_{1}}+2 \overrightarrow{e_{2}}$.

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