
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 $f(x) = e^x + mx - 3$, find the equation of the tangent line to the curve $y = f(x)$ at the point $(0, f(0))$ that has a slope of $-2$.
(I) Determine the intervals where the function $f(x)$ is increasing or decreasing.
(II) When $x > 0$, if the inequality $(t-x)e^x < t + 2$ always holds, find the maximum integer value of the real number $t$.

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