
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
If the tangent line of the curve $f\left(x\right)=\left(ax-1\right)e^{x-2}$ at point $\left(2,f\left(2\right)\right)$ passes through the point $\left(3,2\right)$, then the value of the real number $a$ is ______.

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