
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 curve $f(x) = be^x + x$, the equation of the tangent line at $x = 0$ is $ax - y + 1 = 0$.
(1) Find the values of $a$ and $b$;
(2) When $x_2 > x_1 > 0$, the inequality $f(x_1) - f(x_2) < (x_1 - x_2)(mx_1 + mx_2 + 1)$ always holds. Find the range of the real number $m$.

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