
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

Observe that $(x+2)^{3}=x^{3}+6x^{2}+12x+8$ and

$$
x^{3}+6x^{2}+12x+8 < x^{3}+8x^{2}+42x+27 < x^{3}+12x^{2}+48x+64 = (x+4)^{3}
$$

Therefore,

$$
y=x+3
$$

$(x+3)^{3} = x^{3}+9x^{2}+27x+27 = x^{3}+8x^{2}+42x+27$

Solve for $x$ if $x^{2}=15x$.

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