
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 inequality $x^2 - 3x + t < 0$ has the solution set $\{x | 1 < x < m, x \in \mathbb{R}\}$  
(1) Find the values of $t$ and $m$;  
(2) If the function $f(x) = -x^2 + ax + 4$ is increasing on the interval $(-\infty, 1]$, find the solution set of the inequality $\log_a (-mx^2 + 3x + 2 - t) < 0$.

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