
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
At time $t=0$, a ball is thrown downward at 32 feet per second from a height of 180 feet above the ground. The ball was actually released 1 second after a mechanism activated. The height $h$ of the ball in feet, after activation of the mechanism, is described by the equation $h = -16(t-1)^2 - 32(t-1) + 180$. Find out how many seconds after t = 0 will the ball hit the ground (express time as a decimal).

Present the answer in LaTex format: \boxed{Your answer}
user