
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 the sequence {$a_n$} defined by
$$
a_n= \begin{cases}
-1 & \text{if the } n^\text{th} \text{ draw is a red ball} \\
1 & \text{if the } n^\text{th} \text{ draw is a white ball}
\end{cases}
$$
and let $S_n$ be the sum of the first $n$ terms of the sequence {$a_n$}, determine the probability that $S_7 = 3$.

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