
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 $\mathbf{a} = (1, 2)$, $\mathbf{b} = (1, 0)$, $\mathbf{c} = (3, 4)$. If $\lambda$ is a real number, and $(\mathbf{a} + \lambda\mathbf{b}) \parallel \mathbf{c}$, then $\lambda =$

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