
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 $y=e^x$, the tangent line at the point $(a_k, e^{a_k})$ intersects the x-axis at the x-coordinate $a_{k+1}$, where $k \in \mathbb{N}^*$, and $a_1 = 0$, find the sum of $a_1 + a_3 + a_5$.

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