
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 two infinite sequences $\{a\_n\}$ and $\{b\_n\}$, let $A = \{x | x = a\_n, n \in \mathbb{N}^*\}$, $B = \{x | x = b\_n, n \in \mathbb{N}^*\}$. If the following conditions are simultaneously satisfied: 1) $\{a\_n\}$, $\{b\_n\}$ are both strictly increasing; 2) $A \cap B = \varnothing$ and $A \cup B = \mathbb{N}^*$, then $\{a\_n\}$ and $\{b\_n\}$ are called infinite complementary sequences.

1. If $a\_n = 2n - 1$, $b\_n = 4n - 2$, determine whether $\{a\_n\}$ and $\{b\_n\}$ are infinite complementary sequences and explain the reason.
2. If $a\_n = 2^n$ and $\{a\_n\}$ and $\{b\_n\}$ are infinite complementary sequences, find the sum of the first 16 terms of $\{b\_n\}$.
3. If $\{a\_n\}$ and $\{b\_n\}$ are infinite complementary sequences, $\{a\_n\}$ is an arithmetic sequence with $a\_16 = 36$, find the general terms of $\{a\_n\}$ and $\{b\_n\}$.

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