
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 the vector $\overrightarrow{a} = (-4, 3)$, and points $A(-1, 1)$ and $B(0, -1)$ whose projections on $\overrightarrow{a}$ are $A_1$ and $B_1$ respectively. If $\overrightarrow{A_{1}B_{1}} = \lambda \overrightarrow{a}$, calculate the value of $\lambda$.

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