
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 certain company implements an annual salary system, where an employee's annual salary consists of three components: basic salary, housing allowance, and medical expenses, as specified below:

| Item          | Salary in the First Year (in ten thousand yuan) | Calculation Method After One Year |
|---------------|--------------------------------------------------|-----------------------------------|
| Basic Salary  | $1$                                              | Increases at the same rate each year |
| Housing Allowance | $0.04$                                       | Increases by $0.04$ each year |
| Medical Expenses | $0.1384$                                      | Fixed and unchanged |

(1) Let the annual growth rate of the basic salary be $x$. Express the basic salary in the third year in terms of $x$.

(2) A person has been working in the company for $3$ years. He calculated that the sum of the housing allowance and medical expenses he received in these $3$ years is exactly $18\%$ of the total basic salary for these $3$ years. What is the annual growth rate of the basic salary?

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