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世界の動きを見ると、日本の経済はますます厳しくなっていきそうですが、新しいことにどんどんチャレンジしていくつもりです。

First, my attempt at translation: "When I look at the worlds development, even though we seem to enter a time in which Japans economy becomes harder, I want to rapidly challenge new things."

My main issue lies with the parts in bold. First, I don't know how to interprete this 行く in チャレンジしていく. I know of two ways to interprete this 行く, one is in the way I did it in the first half of the sentence where it marks that change will happen in a timespan starting now/soon, and one is that VERB is pointing in the direction away from the speaker. The latter doesn't seem to make any sense to me, but I also have problems "adding" the "I want to" from つもりです to the チャレンジしていく group which already points into the future. I also don't feel too confident about my interpretation of に in relation to チャレンジしていく.

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You got this. つもり is sort of intensifying the speaker's resolve. As in, "I resolve to continue steadily facing new challenges." していく means "doing now and continuing to do so into the future." It doesn't have to represent a change. 雨が降っていく means it's raining now and it's going to keep raining.

Also, there's no sense of "entering" a time when Japan's economy is rough. I would translate the sentence as follows:

"Looking at world trends, even though it looks like Japan's economy will continue to suffer, we resolve to continue challenging ourselves to do new things."

Or maybe "...continue to take on new challenges."

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