to take no sides / not to take sides

From Cambridge Certificate of Proficiency in English 2:

Complete the second sentence so that it has a similar meaning to the first sentence, using the word given.

William tried to remain impartial in the quarrel between his two cousins.

sides

William tried ............... in the quarrel between his two cousins.

I thought that, 'William tried to take no sides in the quarrel between his two cousins' sounded OK, but the key suggests 'William tried not to take sides in the quarrel between his two cousins.'

I have found two citations in Google Books of "to take no sides", here and here. Nevertheless, it doesn't appear to be a common structure.

What do you think? Is my sentence acceptable?

Thank you in advance.

Chicken Sandwich said:

From Cambridge Certificate of Proficiency in English 2:

Complete the second sentence so that it has a similar meaning to the first sentence, using the word given.

William tried to remain impartial in the quarrel between his two cousins.

sides

William tried ............... in the quarrel between his two cousins.

I thought that, 'William tried to take no sides in the quarrel between his two cousins' sounded OK, but the key suggests 'William tried not to take sides in the quarrel between his two cousins.'

I have found two citations in Google Books of "to take no sides, here and here. Nevertheless, it doesn't appear to be a common structure.

What do you think? Is my sentence acceptable? Acceptable? Yes. More common? No.

Thank you in advance.

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b.