
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
Consider an inifinte sequence  $x_1, x_2,\dots$  of positive integers such that, for every integer  $n\geq 1$ :
 
- If  $x_n$  is even,  $x_{n+1}=\dfrac{x_n}{2}$ ;
- If  $x_n$  is odd,  $x_{n+1}=\dfrac{x_n-1}{2}+2^{k-1}$ , where  $2^{k-1}\leq x_n<2^k$ .

Determine the smaller possible value of  $x_1$  for which  $2020$  is in the sequence.

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