
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 \( f(1)=1, f(2)=2 \) and satisfy the following condition:
$$
f(n+2) \geq 2 f(n+1) - f(n) \quad \forall n \in \mathbf{N}^{+}.
$$

Find \( f(n) \).

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