The people exercise their authority by:

Make sure your instructions are clear

Having ambiguous goals, or methods of achieving them, automatically undermines your authority and dooms many projects from the beginning.  Rule #1 - be clear on the goal and the instructions on how to accomplish it.  After you have delivered them, ask your team if they have any questions about what is required, so problems can be cleared up from the beginning.

Encourage people to approach you if they run into problems

Establishing open communication and feedback early on is crucial to avoid big disappointments later.

Helping team members resolve problems as they arise ensures quick resolution, continued progress, and good morale.

Take action quickly when you learn of any real problems

Failing to act quickly once you learn of a problem, or putting it off for days or weeks, not only undermines your authority, but also kills morale and confidence. Problems tend to get bigger the longer they go unresolved, and your job as a leader is to solve problems not avoid them.

Insist your team report all the news - good and bad

So many companies treat bad news like the plague.

Teams are taught to "always be positive", but an attitude of "always be accurate and let's find a way to succeed", is more productive (and realistic). In meetings and one-on-ones, your goal should be to motivate as well as problem solve. Always encourage your team to report all the news.

Use crises as an opportunity to develop people

You are a leader for a reason!

Rather than shy away from a crisis (a big deal lost, unexpected bad news, major delay, etc.), teach your team members how to find opportunity in crises and how to grow as professionals and as people. Focus on the skills or attitudes that are needed to overcome the situation, and work with them to develop and strengthen them.

Explanation:

what are the options?