
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 \( f(x) \) is such that for all \( x \), the equation \( f(x+1) = f(x) + 2x + 3 \) holds. It is known that \( f(0) = 1 \). Find \( f(2012) \).

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