
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
The data of the height of a certain ball falling and the height of its rebound are shown in the table below, where $x$ represents the height of the ball falling and $h$ represents the height of the ball after landing (unit: $cm$).

| $x/cm$ | $\ldots $ | $10$ | $30$ | $50$ | $70$ | $\ldots $ |
|--------|-----------|------|------|------|------|-----------|
| $h/cm$ | $\ldots $ | $5$  | $15$ | $25$ | $35$ | $\ldots $ |

$(1)$ What relationship between which two variables is reflected in the table?  
$(2)$ Based on the data in the table, write the analytical expression of the function between $h$ and $x$, and calculate the height of the ball after landing when $x=90$.

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