Here's a breakdown:
* "I think" - This phrase expresses the speaker's opinion or belief.
* "it would be best" - This indicates that the speaker believes the proposed action is the most advantageous or beneficial option.
* "to study the problem carefully" - This specifies the action being proposed. It implies a need for thorough investigation and analysis of the problem before attempting to solve it.
Therefore, the overall purpose of the sentence is to recommend careful consideration and analysis of the problem before taking any further steps.