
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 sequence consists of 19 ones and 49 zeros arranged in random order. We define a group as the maximal subsequence of identical symbols. For example, in the sequence 110001001111 there are five groups: two ones, followed by three zeros, then one one, then two zeros, and finally four ones. Find the expected length of the first group.

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