
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
Take the number   $2^{2004}$  and calculate the sum   $S$  of all its digits. Then the sum of all the digits of   $S$  is calculated to obtain   $R$ . Next, the sum of all the digits of  $R$ is calculated   and so on until a single digit number is reached. Find it.  (For example if we take    $2^7=128$ , we find that    $S=11,R=2$ . So in this case of    $2^7$  the searched digit will be  $2$ ).

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