
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
A partition of a positive integer is even if all its elements are even numbers. Similarly, a partition
is odd if all its elements are odd. Determine all positive integers  $n$  such that the number of even partitions of $n$  is equal to the number of odd partitions of  $n$ .
Remark: A partition of a positive integer  $n$  is a non-decreasing sequence of positive integers whose sum of
elements equals  $n$ . For example,  $(2; 3; 4), (1; 2; 2; 2; 2)$  and  $(9) $  are partitions of  $9.$ 

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