
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
There are two red balls and one white ball of the same size in a pocket. Balls are drawn with replacement, and a sequence $\{a\_n\}$ is defined as follows: $a\_n=\begin{cases} -1, \text{if a red ball is drawn on the nth draw}, \\ 1, \text{if a white ball is drawn on the nth draw}. \end{cases}$ If $S\_n$ is the sum of the first $n$ terms in the sequence $\{a\_n\}$, what is the probability that $S\_7=3$?

A) $\frac{26}{3^{6}}$
B) $\frac{28}{3^{6}}$
C) $\frac{29}{3^{6}}$
D) $\frac{31}{3^{6}}$

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