
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
If \( x \) satisfies \( x^2 + 4x + \frac{4}{x} + \frac{1}{x^2} = 35 \) and \( x \) can be written as \( a + \sqrt{b} \) where \( a \) and \( b \) are positive integers, find \( a + b \).

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