
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 a point $A(1,0)$, a curve $C:y=x^{m}$ where $x>0$, $m>1$, and $m\in N^{*}$, find the tangent line to the curve passing through point $A$. Let $B_{1}$ be the point of tangency, and let $A_{1}$ be the projection of $B_{1}$ onto the $x$-axis. Similarly, find the tangent line to curve $C$ passing through point $A_{1}$, let $B_{2}$ be the point of tangency, and let $A_{2}$ be the projection of $B_{2}$ onto the $x$-axis. This process continues to obtain a series of points $B_{1}$, $B_{2}$, $\ldots$, $B_{n}$, where the $x$-coordinate of point $B_{n}$ is denoted as $a_{n}$. Find the values of $a_{1}$ and $a_{2}$.

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