
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 the function $f(x) = \log_a(x + 1)$, $g(x) = 2\log_a(2x + t)$ ($t \in \mathbb{R}$), where $x \in [0, 15]$, $a > 0$, and $a \neq 1$.

(1) If $1$ is a solution to the equation $f(x) - g(x) = 0$, find the value of $t$;  
(2) When $0 < a < 1$, the inequality $f(x) \geq g(x)$ always holds, find the range of values for $t$.

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