
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
In the process of deriving the sum of the first \\(n\\) terms of an arithmetic sequence, we used the method of adding in reverse order. By analogy, we can find the sum \\(\sin ^{2}1^{\circ}+\sin ^{2}2^{\circ}+\ldots+\sin ^{2}89^{\circ}=\\) ______.

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