
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 that binary and decimal numbers can be converted to each other, for example, 89=1×2<sup>6</sup>+0×2<sup>5</sup>+1×2<sup>4</sup>+1×2<sup>3</sup>+0×2<sup>2</sup>+0×2<sup>1</sup>+1×2<sup>0</sup>, the decimal number 89 is converted to the binary number (1011001)<sub>2</sub>. Let a<sub>n</sub> represent the number of 0s in the binary number corresponding to n (for example: 4=(100)<sub>2</sub>, 51=(110011)<sub>2</sub>, 89=(1011001)<sub>2</sub>, then a<sub>4</sub>=2, a<sub>51</sub>=2, a<sub>89</sub>=3). Let f(n) = $2^{a_{n}}$, then f(2<sup>2018</sup>) + f(2<sup>2018</sup>+1) + f(2<sup>2018</sup>+2) + … + f(2<sup>2019</sup>−1) = \_\_\_\_\_\_.

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