
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 vectors $\vec{a}=(\sin x,2)$ and $\vec{b}=(\cos x,1)$, satisfying $\vec{a}\parallel\vec{b}$, then $\dfrac{2\sin\left(x+\dfrac{\pi}{4}\right)}{\sin x-\cos x}=$\_\_\_\_\_\_\_\_\_.

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