
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
Determine the difference between the larger root and the smaller root of the equation \[(5+3\sqrt{2})x^2 + (3+\sqrt{2})x - 1 = 0.\]
A) $1 + \sqrt{2}$
B) $2$
C) $2 - \sqrt{2}$
D) $3$
E) $4 - 2\sqrt{2}$

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