
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
A positive number has two square roots, which are opposite to each other. For example, if $x^{2}=9$, then $x=3$ or $x=-3$.  
$(1)$ According to the meaning of the square roots mentioned above, find the solutions to the equation $\left(x-1\right)^{2}=49$.  
$(2)$ The relationship between the height $h$ (in meters) of a freely falling object and the time $t$ (in seconds) of falling is $h=4.9t^{2}$. If an object falls freely from a height of $10$ meters above the ground, find the time it takes for the object to reach the ground.

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