
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 arithmetic sequence $\{a\_n\}$ that satisfies $a\_1 + a\_2 = 10$, and $a\_4 - a\_3 = 2$.
1. Find the general term formula for $\{a\_n\}$.
2. Suppose the geometric sequence $\{b\_n\}$ satisfies $b\_2 = a\_3$, and $b\_3 = a\_7$. What is the term of the arithmetic sequence $\{a\_n\}$ that is equal to $b\_4$?

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