Assume the asset price $S_t$ follows a Geometric Brownian Motion (GBM): $dS_t = rS_t dt + \sigma S_t dW_t$, where $r$ is a constant drift rate, $\sigma$ is a constant volatility, and $W_t$ is a standard Brownian Motion. Now consider a new stochastic process $Y_t = \ln(S_t^2 + t)$. Using Ito's Lemma, derive the Stochastic Differential Equation (SDE) for $Y_t$. Walk me through your detailed derivation and explain your reasoning for each step.

假设资产价格 $S_t$ 遵循一个几何布朗运动 (GBM)：$dS_t = rS_t dt + \sigma S_t dW_t$，其中 $r$ 是常数漂移率，$\sigma$ 是常数波动率，$W_t$ 是标准布朗运动。 现在考虑一个新的随机过程 $Y_t = \ln(S_t^2 + t)$。请使用 Ito 引理推导 $Y_t$ 所满足的随机微分方程 (SDE)。你需要展示详细的推导过程，并清晰地指出每个步骤的依据。