
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 Hailstone conjecture states: for a positive integer $x$, if it is odd, multiply by $3$ and add $1$, if it is even, divide by the largest power of $2$, after several iterations, it will eventually return to $1$. This problem has puzzled many professional mathematicians for over eighty years. Given a sequence of positive integers $\{a_{n}\}$ that satisfies the recursive formula ${a_{n+1}}=\left\{{\begin{array}{l}{3{a_n}+1,\frac{{{a_n}}}{2}∉{N^*}}\\{\frac{{{a_n}}}{2},\frac{{{a_n}}}{2}∈{N^*}}\end{array}}\right.$, please find the initial term $a_{1} \lt 50$ that satisfies $a_{10}=1$, while $a_{i}\neq 1$ for $i=1,2,\cdots ,9$.

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