
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
Let  $S_n$  be number of ordered sets of natural numbers  $(a_1;a_2;....;a_n)$  for which  $\frac{1}{a_1}+\frac{1}{a_2}+....+\frac{1}{a_n}=1$ . Determine 
1) $S_{10} mod(2)$ .
2) $S_7 mod(2)$ .

(1) is first problem in 10 grade, (2)- third in 9 grade.

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