
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
Let $x$ be the least real number greater than $1$ such that $\cos(3x) = \sin(x^3 - 90^\circ)$, where all angles are in degrees. Determine $x$ rounded up to the nearest integer.
**A)** $6$
**B)** $7$
**C)** $9$
**D)** $10$
**E)** $11$

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