
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
We say that a binary string  $s$  *contains* another binary string  $t$  if there exist indices  $i_1,i_2,\ldots,i_{|t|}$  with  $i_1 < i_2 < \ldots < i_{|t|}$  such that   $$ s_{i_1}s_{i_2}\ldots s_{i_{|t|}} = t. $$   (In other words,  $t$  is found as a not necessarily contiguous substring of  $s$ .) For example,  $110010$  contains  $111$ . What is the length of the shortest string  $s$  which contains the binary representations of all the positive integers less than or equal to  $2048$ ?

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