
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 that $a, b \in \mathbb{R}$, the function $f(x) = \frac{4 \cdot 3^x + a}{3^x + 1}$ satisfies $y = f(x) - b$ as an odd function.

1. Find the relationship between the real numbers $a$ and $b$.
2. When $b = 3$, if the inequality $f(\log_5{t}) > \frac{5}{2}$ holds, find the smallest integer value that the real number $t$ can take.

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