
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

Alice enters a website name in her browser. This name is sent over the network to a special DNS server, which determines its IP address - a set of four integers \(X_1 \cdot X_2 \cdot X_3 \cdot X_4\), where \(0 < x_i < 255, i=1,2,3,4\). The server sends this IP address to Alice along with a number \(s\), which is calculated as follows: \(s = r_{305}\left(\left(h_4\right)^d\right)\), where \(d\) is a secret natural number known only to Alice and the server, and \(r_{305}(x)\) is the remainder of dividing \(x\) by 305; the number \(h_4\) is determined by sequentially applying the rule \(h_i = r_{305}\left(\left(h_{i-1}\right)^2 \cdot x_i\right)\), where \(i\) takes values 1,2,3,4, and \(h_0 = 1\). Upon receiving the IP address, Alice also calculates \(s\). If it matches the value sent by the server, Alice accepts the IP address as authentic. An attacker found out that in response to Alice's request, the server replied with: 10.11.1.1 with \(s = 15\). He wants to send Alice a false (different from the original) address of the form 10.11.a.b and a number \(s'\) so that Alice recognizes this address as authentic. Find at least one such triplet \(a, b, s'\) with the condition \(s' \geq 1\).

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