
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
Define an odd function $f(x)$ on $\mathbb{R}$ satisfying $f\left(x+ \frac{5}{2}\right) = -\frac{1}{f(x)}$. If $f(1) \geq 1$ and $f(2014) = \frac{t+3}{t-3}$, then the range of the real number $t$ is ______.

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