
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 recurrence relation $F(n+1) = \frac{2F(n) + 3}{2}$ for $n = 1, 2, ...,$ starting with the condition $F(1) = 3$, determine $F(101)$. Additionally, describe the behavior of $F(n)$ as $n$ approaches infinity.
A) 150
B) 151
C) 152
D) 153
E) 154

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