
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
The function $y=x^{2}$ ($x > 0$) has a tangent line at the point $(a_{k},a_{k}^{2})$ that intersects the $x$-axis at the abscissa $a_{k+1}$, where $k$ is a positive integer, and $a_{1}=16$. Calculate the value of $a_{1}+a_{3}+a_{5}$.

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