
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: $\mathbf{\vec{a}}_1, \mathbf{\vec{a}}_2, \mathbf{\vec{a}}_3, \cdots, \mathbf{\vec{a}}_n, \cdots$ satisfying the following conditions: $|\mathbf{\vec{a}}_1|=2$, $|\mathbf{\vec{d}}|=\frac{\sqrt{2}}{4}$, $2\mathbf{\vec{a}}_1 \cdot \mathbf{\vec{d}}=-1$ and $\mathbf{\vec{a}}_n-\mathbf{\vec{a}}_{n-1}=\mathbf{\vec{d}} (n=2,3,4,\cdots)$. Then, among $|\mathbf{\vec{a}}_1|, |\mathbf{\vec{a}}_2|, |\mathbf{\vec{a}}_3|, \cdots, |\mathbf{\vec{a}}_n|, \cdots$, the $\boxed{\text{5th}}$ item is the smallest.

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