
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
Let real numbers \(a\) and \(b\) satisfy \(a + b = 5\) and \(ab = 1\). Find the value of 
\[a + \frac{a^3}{b^2} + \frac{b^3}{a^2} + b.\]
A) 2500
B) 2525
C) 2535
D) 2550
E) 2600

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