
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 $f(x) = e^x + ae^{-x}$ (where $a \in \mathbb{R}$), its derivative $f'(x)$ is an odd function. If the slope of a tangent line to the curve $y = f(x)$ is $\frac{3}{2}$, then determine the coordinates of the point of tangency.

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