
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
Six statements are made about a natural number \( x \):

$$
\begin{aligned}
& 3x > 91 \\
& x < 120 \\
& x < 27 \\
& 4x > 37 \\
& 2x \geq 21 \\
& x > 7
\end{aligned}
$$

It is known that exactly three of these statements are true, and three are false. Find \( x \).

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