
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 $f(1,1)=1$, $f(m,n) \in \mathbb{N}^*$ ($m,n \in \mathbb{N}^*$), 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) $f(5,6) = 26$.  
The number of correct statements is    ．

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