
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
What real number is equal to the expression $3 + \frac{4}{1 + \frac{4}{3 + \frac{4}{\frac{1}{2} + \cdots}}}$ where the pattern of denominators alternates between a constant and a term from the sequence $\frac{1}{n}$, with $n$ starting at $2$?

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