
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 a sequence of vectors $\overrightarrow{a_1}, \overrightarrow{a_2}, \overrightarrow{a_3}, \ldots, \overrightarrow{a_n}, \ldots$ satisfying the condition $\overrightarrow{a_n} - \overrightarrow{a_{n-1}} = \overrightarrow{d}$ (for $n=2,3,4,\ldots$), and the angle between $\overrightarrow{d}$ and $\overrightarrow{a_1}$ is $\frac{2\pi}{3}$. Given that $|\overrightarrow{a_1}| = 4|\overrightarrow{d}| = 2$, determine the smallest term in the sequence $|\overrightarrow{a_1}|, |\overrightarrow{a_2}|, |\overrightarrow{a_3}|, \ldots, |\overrightarrow{a_n}|, \ldots$.

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