
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 \(a, b, c, d\) be integers. The four equations involving \(x\):
\[
\begin{array}{rr}
(a-2b)x=1, & (b-3c)x=1, \\
(c-4d)x=1, & x+100=d,
\end{array}
\]
have positive roots. Find the smallest possible value of \(a\).

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