
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 vectors $\mathbf{a} = (1, -3)$ and $\mathbf{b} = (4, 2)$. If $\mathbf{a}$ is perpendicular to $\mathbf{b} + \lambda\mathbf{a}$, where $\lambda \in \mathbb{R}$, find the value of $\lambda$.

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