
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
An arithmetic sequence has $2n$ terms. If $a_1+a_3+\ldots+a_{2n-1}=90$, $a_2+a_4+\ldots+a_{2n}=72$, and $a_1-a_{2n}=33$, then the common difference of the sequence is.

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