
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
Given that $E, U, L, S, R, T$ represent the numbers $1, 2, 3, 4, 5, 6$ (with each letter representing a different number), and satisfying the following conditions:
(1) $E + U + L = 6$
(2) $S + R + U + T = 18$
(3) $U \times T = 15$
(4) $S \times L = 8$

What is the six-digit number $\overline{EULSRT}$?

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