
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
Let \( 0 < a < 1 \), and let \( b = 1 - a \). The inequality \( \mathrm{e}^{x} \leq \frac{1+ax}{1-bx} \) holds for all \( x \in [0, 1] \). Find the maximum value of \( a \).

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