
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
The function \( f \) satisfies
\[
f(x) + f(2x + y) + 5xy = f(3x - y) + 2x^2 + 1
\]
for all real numbers \( x \) and \( y \). Determine the value of \( f(10) \).

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