On properties of symmetric i.i.d ramdom walks

Question

I am currently trying to prove the reflection principle, using step by step instrucions. Let $X_i,\forall i\in\mathbb{N}$ be i.i.d. distributed, real, symmetricly distributed random variables. Define $S_n=\sum_{i=1}^n X_i$ and $N=\inf \{m\leq n:S_m>a\}$. In the first step I showed, that for all $Z$ with symmetric distribution, $P(Z\geq 0)\geq \frac{1}{2}$. In the second step I am supposed to decompose $\{S_n\geq a\}$ using values of $N$. However, I do not know, what it means to decompose using values of N, so I am stuck. Any help or explanations would be appreciated!