
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 segment is divided in such a way that the smaller part is to the larger part as the larger part is to the whole segment, find the value of 
$$
R^{\left[R^{\left(R^{2}+\frac{1}{R}\right)}+\frac{1}{R}\right]}+\frac{1}{R}$$

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