
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
Given $a \in (0, +\infty)$, the function $f(x) = ax^2 + 2ax + 1$. If $f(m) < 0$, compare the size of $f(m + 2)$ and $1$ (use "<", "=", or ">" to connect).

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