
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
Toss a fair coin, where the probability of getting heads or tails is $\dfrac{1}{2}$. Repeatedly tossing the coin, define the sequence $\{a_n\}$ as: $a_n= \begin{cases} 1 & (\text{if the } n\text{th toss is heads}) \\ -1 & (\text{if the } n\text{th toss is tails}) \end{cases}$. If $S_n=a_1+a_2+\ldots+a_n$ ($n\in\mathbb{N}^*$), calculate the probability of the event $S_4 > 0$.

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