
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
Suppose we have the function $f(x) = ax^2 + x$. It is known that $f(3) < f(4)$, and for all natural numbers $n \geq 8$, $f(n) > f(n+1)$ holds true. Determine the range of the real number $a$.

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