
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 $f(x) = e^x + \frac{a}{e^x}$, its derivative $f'(x)$ is an odd function. If the tangent line to the curve $y=f(x)$ at the point $(x_0, f(x_0))$ is perpendicular to the line $\sqrt{2}x + y + 1 = 0$, find the y-intercept of this tangent line.

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