
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 the odd function $f(x)$ have the domain $(-\infty, 0) \cup (0, +\infty)$, and be increasing on $(0, +\infty)$.

(1) If $f(1) = 0$, solve the inequality $f(1 + \log_a x) > 0$ ($0 < a < 1$).

(2) If $f(-2) = -1$, and for $m > 0$, $n > 0$, it always holds that $f = f(m) + f(n)$, find the range of $t$ for which $|f(t) + 1| < 1$.

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