Final answer:
A government institution that relies on reasoned analysis to resolve disputes is a court. Courts interpret laws, handle disputes, and maintain checks and balances by potentially voiding unconstitutional laws and policies from other government branches.
Step-by-step explanation:
A government institution that relies upon reasoned analysis in order to resolve disputes and solve problems is: a) A court. Courts are established to interpret and apply the laws of a country and address various types of disputes, including criminal, civil, and sometimes constitutional issues. In the United States, the Supreme Court has the power to void laws and policies from the legislative and executive branches when those are found unconstitutional. Courts are crucial in their role to deliver justice and tend to have a narrower focus on specific cases compared to other branches of government, such as the legislature and the executive, which are concerned with broader policy matters.
Courts are considered the judicial branch of government and work alongside the legislative and executive branches, forming the three formal branches of a country's government. The judiciary's ability to review laws and declare acts of other branches unconstitutional is a key component of the checks and balances system designed to maintain a fair and democratic society.