
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 $a_{1}=2$, $a_{2}=4$, $a_{3}=8$, $a_{4}=16$, for any $b_{1}$, $b_{2}$, $b_{3}$, $b_{4} \in \mathbb{R}$, if $\{a_{i}+a_{j} | 1 \leq i < j \leq 4\} = \{b_{i}+b_{j} | 1 \leq i < j \leq 4\}$, find the number of ordered sequences $\{b_{1}, b_{2}, b_{3}, b_{4}\}$.

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