
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 tangent line of the graph of the function $y=x^2$ $(x > 0)$ at the point $(a_n, a_n^2)$ intersects the $x$-axis at a point with the $x$-coordinate $a_{n+1}$, where $n$ is a positive integer. If $a_1=16$, then find the value of $a_1 + a_3 + a_5$.

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