
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 a fair coin is tossed with the probability of landing on heads or tails both being $\frac{1}{2}$, and the sequence $\{a_n\}$ is defined as: $$a_{n}= \begin{cases} 1 & \text{(the $n^{th}$ toss is heads)} \\ -1 & \text{(the $n^{th}$ toss is tails)}\end{cases}$$ calculate the probability of the event $S_4 > 0$, where $$S_{n}=a_{1}+a_{2}+\ldots+a_{n} \quad (n\in\mathbb{N}^{+}).$$

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