
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 $f(1,1)=1$, $f(m,n) \in \mathbb{N}^*$ for all $m,n \in \mathbb{N}^*$, and for any $m,n \in \mathbb{N}^*$, the following conditions hold:

(1) $f(m,n+1)=f(m,n)+2$.

(2) $f(m+1,1)=2f(m,1)$.

Consider the following three statements: ① $f(1,5)=9$; ② $f(5,1)=16$;

③ $f(5,6)=26$. Among these, the correct statement(s) is/are.

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