
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 a geometric sequence $\{a_n\}$ where $a_1=2$ and $a_1+a_2=6$. Find the sum of the first $n$ terms of the sequence, $S_n$.  
(2) Given $\tan \theta=3$, find the value of $\dfrac {2\cos ^{2} \dfrac {\theta}{2}+\sin \theta-1}{\sin \theta-\cos \theta}$.

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